Unlike metahumans who develop their powers only after exposure to outside stimuli or energies to effect their DNA (such as Hulk, Spider-Man, and the Fantastic Four), mutants are born with the genetic potential to possess their powers, although the powers typically manifest at puberty.
The initial causes for the X-Gene mutations are currently unknown. The effects of the gene itself vary from one individual to another, to the point that it's not uncommon that even amongst blood-related mutants, they possess different abilities from one to another (such as the case of Magneto and his twin children, Wanda and Pietro).
The external physiology of the mutants is also altered to varying degrees. Some of them, like Scott Summers and Jean Grey, don't suffer external changes, thus allowing them to pass off as normal humans. Others, like Lorna Dane only suffer minor changes that are relatively easy to hide (in her case, an abnormal hair color), while others such as Kurt Wagner or the Morlocks, have their appearances radically altered to the point they are unable to blend in at all.
As the physiology of mutants still remains essentially "human", they are capable of interbreeding with normal people, and their children will still carry on the X-Gene to their descendants.
Omega Level Mutant is a term that is commonly used to refer to a mutant possessing powers without foreseeable limits.
Alpha Level Mutants are powerful mutants who mastered their abilities.
Mutants are one of the most common of characters from the Marvel Universe and made up into various groups and organizations. Although some do exist in the DC universe but the majority of them gain their powers from accidents and genetic experiments. Both are treated different in both realities; the Marvel mutants are treated harshly for being non-humans and are continuously threatened to be registered for their powers and controlled. While some in DC are seen as any other heroes and villains by the population and much the opposite as their counterparts.