Soil Horizons are the distinct layers of a soil profile. They are divided into these layers, referred to as "Master Horizons" (from top to bottom): O Horizon, A Horizon, E Horizon, B Horizon, C Horizon, and R Horizon. There also exists an H Horizon, F Horizon, and an L Horizon, each of which revolve around organic material, somewhat similarly to the O Horizon, but with more specific qualities and generally more obscure. The number and composition of horizons in different soils has tremendous diversity; the most well-developed soils might have all of these layers, and the least-developed soils might only have an A and a D horizon.
Main Master Horizons
Master Horizons are the main layers of a soil profile, described below.
The O Horizon is composed of organic material that has accumulated and been modified (physically and chemically) over time, typically from the remains of plant and animals . This horizon is most easily observed in soils that are rarely, if ever, disturbed and with plenty of foliage and/or organisms nearby to contribute to its development, such as forests. In more barren locations such as grasslands, an O Horizon is rarer.  Due to the fact that its presence is determined by external factors (outside of the original parent materials that form soils), it is the only layer not dominated by mineral substances. This layer has three well-accepted subordinate horizons: Oi (slightly decomposed organic matter), Oe (moderately decomposed organic matter), and Oa (highly decomposed organic matter).  Microbial activity is high in this layer, utilizing the abundance of organic matter and decomposing it in ways that allow it to contribute to the soil profile.
The A Horizon is a well-weathered and fertile layer dominated by mineral particles but still rich in organic matter, especially if covered by an O Horizon, which can leach decomposed organic matter into the A Horizon. This is a much thicker layer than the O Horizon, dominated by highly weathered mineral particles (the most highly weathered from the parent material of the soil), and typically darker and coarser than other Soil Horizons. (Elements pg. 53) The A Horizon is considered topsoil. If this layer has properties of both an A and an E Horizon, it is considered an A Horizon if it is dominated by humidified organic matter.  Subterranean life (including microfauna, mesofauna, and macrofauna) tends to be the most abundant in this layer due to the rich, soft, and well-weathered environment of the soil.
The E in "E Horizon" stands for eluviation, another word for leaching. This name is appropriate because, in this layer clay, iron, and aluminum oxides leach into the lower layers (mostly the B Horizon).  Like the O Horizon, this layer is not always present, but when it is, it's usually in forested areas and rarely in grasslands. Because of the loss of material through eluviation, it tends to be noticeably lighter than the layers above and below it. 
The B Horizon is also known as the subsoil. B Horizons are often greatly composed of material illuviated (washed in from) layers above it, mostly clay, iron, aluminum oxides (deposited by elluviated water), and minerals that formed in the layer. 
The C Horizon, also known as the substratum is unconsolidated material above bedrock.  It is insufficiently weathered to be considered soil, but still considered a layer of a soil profile. Subterranean life is far scarcer in this layer, and plant roots do not usually extend here, although it is usually soft enough for root penetration.  It is essentially a transitional layer from bedrock to the soil.
This layer is simply bedrock with minimal to no weathering visible. It is composed of the parent material that would eventually be transformed into soil. Excavating this horizon generally requires specialized equipment, and roots are usually unable to take advantage of what cracks may be in this layer. This layer is the boundary between what lies beneath the soil. 
Other Master Horizons
These master horizons are dominated by plant-based organic matter in well-drained soils, occurring most commonly in forests.  These layers are generally more obscure than the previously mentioned Soil Horizons due to these specialized circumstances. Also, some may consider these horizons to be Subordinate O Horizons rather than their own Master Horizons.
The L Horizon stands for "Litter Horizon" and is dominated by plant material with minimal to no visible decomposition, with plant elements easy to identify. 
The F Horizon stands for "Fermentation Horizon" and is composed of moderately decomposed plant material, but the plant origins are still distinguishable. 
The H Horizon stands for "Humic Horizon" and is composed of a material that is well humified and decomposed by water, and identifying plant material is difficult. 
Soil Horizons do not always form distinct bands with unique and easily identified properties. Often Soil Horizons form Transitional Horizons, which have two forms.  The first is when a horizon has dominant properties of one Soil Horizon and subordinate properties of another; these Transitional Layers are designated by putting the dominant horizon properties letter first, followed by the subordinate horizon; an example would be a BC horizon, with properties more like a B Horizon but still demonstrating sufficient similarities to a C Horizon.  The second form of a Transitional Horizon is when the properties of both horizons are very comparable in representation; these have the letters separated with a "/", such as a B/C horizon, which is almost equally a B and a C Horizon. 
In order to more accurately describe the characteristics of the master horizons, lowercase letters from the Latin Alphabet are added. depending on the characteristics of the soil. Almost all letters are used, with the exception of l and u. Instead, there are jj and ss distinctions. Subordinate horizon symbols include the following: 
a: Highly decomposed organic matter is present
b: The soil horizon has been buried
c: Concretions/Nodules of Fe, Al, Mn, or Ti cement is present
d: The soil is dense from natural or artificial means, and root access is restricted
e: Moderately decomposed organic matter is present
f: The soil is frozen
g: Strong gleying/mottling is present
h: The organic matter was illuviated
i: Slightly decomposed organic matter is present
j: Jarosite is present
jj: Cryoturbation / Frost churning is present
k: Carbonate buildup is present
m: Continuous cementation is present
n: Sodium buildup is present
o: Iron and Aluminum oxides buildup is present
p: The soil has been heavily disturbed, typically by tillage
q: Silica buildup is present
r: Bedrock is weathered or soft
s: Organic matter and Iron and Aluminum Oxides were illuviated (not to be confused with h and o, which are only organic matter and Iron and Aluminum Oxides, respectively)
ss: Slickensides are present
t: Buildup of silicate clays is present
v: Pilinthe is present
x: Fragipan is present
y: Buildup of gypsum is present
z: Buildup with salts more soluble than gypsum is present
Factors Affecting the Formation of Soil Horizons
Soil Horizon formation depends on many factors, most famously described by Hans Jenny's "fundamental equation": s = f (cl, o, r, p, t, …)
In this equation, soil is described as being a function of climate, organisms, relief/slope, parent material, time, and any other potential factors that he had not considered at the time of the formula's creation. Climate affects the rates of both physical and chemical weathering, Organisms affect the rate of soil formation and contribute organic matter to it, Relief affects the amount of water and erosion in a soil, Parent Material affects the initial properties of developing and mature soils, and time is required for these factors to go into effect and eventually form a soil and its Soil Horizons.  Other factors are almost certain to be contributing as well, but at a negligible or unknown scale.
 Brady, Nile C.; Weil, Ray R.. Elements of the Nature and Properties of Soil. (Second Edition) Pearson Education, Inc. 2004. pg 53-55. Retrieved 2018-03-05.
 Turenne, Jim. Soil Horizons (a Basic Power Point Presentation). Retrieved 2018-03-06. http://nesoil.com/properties/horizons/
 Soils Glossary Appendix. Soil Science Society of America. 2018. Retrieved 2018-03-06 https://www.soils.org/publications/glossary/appendix/
 Food and Agriculture Organization of the United Nations. World reference base for soil resources. Rome 1998. Appendix 1: Soil Horizon Designations. Retrieved 2018-03-07. http://www.fao.org/docrep/W8594E/w8594e0g.htm
 Forest Floor. Soil Horizons. Retrieved 2018-03-07. http://forestfloor.soilweb.ca/definitions/soil-horizons/
 Lamb, John A.; Rehm, George W.. Five factors of soil formation. University of Minnesota. Retrieved 2018-03-07. https://www.extension.umn.edu/agriculture/soils/soil-properties/five-factors-soil-formation/