A mutant is a type of fictional character in a fictional universe created by Marvel Comics. In this world, mutants can be either heroes or villains. A mutant is someone who has different DNA than its parents. These mutations often lead to superpowers. They may also cause physical changes such as wings, blue skin, or a tail.

Mutants were created in the Marvel Universe in the 1960s with the comic book The X-Men. It was a way for them to tell stories that dealt with racism. Racism, hatred and fear of mutants are an important part of their history  . Two main teams of mutants have been around since the 1960s: The X-Men (heroes) and the Brotherhood of Mutants (villains).

Overview

Sometimes a human is born with a certain kind of DNA change. This X-GENE is passed to their children. This genetic change may not create any noticeable difference. It could pass for generations without anyone knowing about it.

Mutants may be born to human or mutant parents, though the odds of a mutant birth are much better for the latter. Likewise, it is rare but possible for mutant parents to have human children, termed "baseline" by characters within the Marvel Universe. Some baseline humans are genetically predisposed towards having mutant descendants such as the Guthrie family (see Cannonball, Husk, and Icarus). Mutant children born to mutant parent(s) will not necessarily have the same power(s) as their parent(s), nor will they necessarily have the same power(s) as any mutant siblings they may have; however, examples of children with the same power(s) as their parents and/or siblings are not uncommon.

There is, however, a chance that mutants may not even be able to reproduce a child at all. The Hayes (Runaways), telepathic mutant doctors, were unsure their mutant heritage could even produce a child; it did, however, take them several years to finally have a child: Molly Hayes.

Classification
Marvel's mutants are classified by their level of power.

OMEGA: Omega mutants are those with the highest level of power. They are the most powerful of the Alphas.
ALPHA: Alpha mutants have very powerful and useful mutant powers and no drawbacks such as changes in appearance. They are perhaps the most feared  mutants.
BETA: Betas are as powerful as alphas but they have some physical changes as a drawback.
GAMMA: Gammas are also powerful mutants but they suffer from large physical changes. These changes make their lives very hard and make them very easy to tell they are a mutant.
DELTA: Delta mutants have low levels of power than Alphas. Like Alphas, they have no physical changes. Most Deltas do not even know they are mutants.
EPSILON: Epsilons have minor superhuman powers and major physical flaws. They are easily recognized just by looking at them.

Note: Only Alpha and Omega have actually been used as classification within comics. The other ranks were created by fans.

Mutants as a metaphor for racism
The X-Men were created in the 1960s during a time of civil unrest in the United States. The characters allowed the writer to write stories that showed racism and bigotry without singling out a specific minority.

By classifying Mutants as they did, they also created different aspects of racism. Some mutants are easily recognized by how they look (similar to African-Americans). Some have a few physical characteristics that can make them get noticed (Similar to Jews). Other mutants blend in so well that it nearly impossible to tell they are a mutant unless they use their powers (similar to how people in the LGBT community were thought of in society).

In the Marvel universe normal people often hate and fear mutants. This is  because they think mutants may make normal humans extinct. They fear what they do not understand. They are jealous of them having superpowers. Bigotry and xenophobia are also reasons for hatred of mutants. In the Marvel universe, anti-mutant feeling has led to the separation of mutants from society. It has led to  mob violence and government sponsored attempts to fight mutants.

The X-Men books have been written as typical superhero comic books. They have epic adventures and battles with super villains. Yet, the idea of mutants as a metaphor for real world minorities who face oppression is shown throughout the series. Some examples:

 Magneto, a Jewish Holocaust survivor who once lived in Israel. He has tried to create a "mutant home state" similar to Israel. He became ruler of Genosha, a fictional island off the coast of Madagascar, recognized by the United Nations as a mutant state.
 The 1981 story set in the future, Days of Futures' Past, shows a mutant Holocaust. Mutants are herded into concentration camps and killed. 
 Senator Robert Kelly has proposed a Mutant Registration Act. It would force mutants to list their powers and identities with the federal government. This is very similar to McCarthyism and other acts of Congress that outlawed the American Communist Party.
 The anti-mutant hate group Friends of Humanity was inspired by the Aryan Nations. Its leader was inspired on Frank Collin, Chairman of the National Socialist (Nazi) Party of America.
 Most mutant powers take effect at puberty. A large number of young mutants are rejected by their families. This is similar to young gay people discovering their homosexuality in their teen years and the rejection they receive from their family.  This is show very openly in the second X-Men movie with the line "Have you ever tried not being a mutant?"
 The Legacy Virus storyline of the 1990s was seen as a metaphor for the AIDS epidemic.

Other websites 
 Marvel Entertainment official site
  

Marvel Comics