Simply put, a model release is a legal contract that "releases" one party from liability for having (potentially) violated the other party's rights. It's almost always used in the context of a photograph. Despite the apparent association with models you see in magazines, the word "model" here is merely the subject of the photo. The Merriam-Webster dictionary's definition for a model is "a representation of something (usually on a smaller scale)." Thus, the subject of a photo is the model: a person, building, article of clothing, painting, and so on. It could be that a release may be necessary to waive whatever rights the model has if the photo is to be used in particular ways.
"What rights are there that can be violated?," you may ask. It turns out that both the subject of the photo and the photographer have rights. On one hand, people have rights concerning how their own likenesses or property are used, so they may choose to permit or deny the use in a photo that has them in it. The purpose of the model release is for the individual to waive the rights in return for compensation. On the other hand, the right of free speech and other uses permitted by the U.S. Constitution (and the laws in most countries that have a free press) override some of those individual rights, in which case, there are some ways that photos can be published without the need for a model release.