There are two major types of snare drum heads: natural animal skin or synthetic. The different styles of snare drum heads within each of these categories provide different sound and rebound characteristics. A drummer thus may choose one type of head for one situation and another drum head for another venue.
Natural animal skin was the "original" drum head, not only for snares, but for other drums, too. It has been used for centuries in countries all over the world. The exact skin used depends on the wild or raised animals available. This has a huge influence over the sound of the drum, because different skins have different thicknesses. Skin snare drum heads were standard until the mid-1950s, with calfskin drum heads probably most common.
One reason why calfskin snare drum heads have fallen somewhat out of favor in the contemporary performance setting is that animal skin is incredibly sensitive to changes in humidity and temperature. That makes it much harder to control not only the pitch of the drum, but the feel of the drum in terms of resistance. Some people do not advocate the use of animal skins out of concern for animal rights, as well. Some groups who strive to provide an authentic sound of older works still use calfskin heads regularly.
In 1956, Chick Evans devised a polyester drum head. The idea was that a synthetic drum head would be both more durable and more stable than traditional animal skin. The following year, Remo Belli and Sam Muchnick developed a head made of biaxially-oriented polyethylene terephthalate (BoPET), which is marketed under brand names such as Mylar® and Melinex®. This type of head quickly gained favor and is one of the two major synthetic snare drum head choices.
The other primary option in the synthetic drum head category is poly-paraphenylene terephthalamide, better known as Kevlar®. Invented in 1964-1965 by polymer scientist Stephanie Kwolek, Kevlar® originally was developed for tires, but development teams quickly saw alternative uses for the material. Snare drum heads made of Kevlar® are among some of the strongest due to the number of bonds Kevlar® has.
In comparing Mylar® and Kevlar®, Mylar® provides more "give." It thus is less taxing on the wrists and hands. The downside of Mylar® is that the "give" the head provides means the drum requires more-frequent tuning. Kevlar® rebounds to a high degree and can withstand high tension, which is desirable in some types of snare drums such as those in marching ensembles. It provides very clean articulation as a result, but the rigidity of the head makes it less suitable for people who do not have absolute control over their technique.
When looking at the various drum head types, it is important to realize that no type of drum head is necessarily better than another. Which drum head to select for the snare is simply a matter of the drummer's sound preference, as well as the drummer's physical needs. Each type of snare drum head has an appropriate musical place.