The X-Men were unusual in the early 1960s for several reasons. They were young, students really, but more importantly they were minorities. They were a comic analogue for the various real-life minorities then (and now) struggling for equality and safety in a society that feared and derided them. The mastermind behind the team was Charles Xavier, a wheelchair-bound professor and strongest telepath on Earth. The obvious early contrast, of course, was the strength of his mind compared to the frailty of his body.
Professor X would be the mutant Dr. King (compared to Magneto's Malcolm X) in the rising tensions between homo sapiens and homo superior. He advocated coexistence, and formed the X-Men not only to provide a haven for young mutants where they could learn to handle their powers, but also as an example to humanity that mutants could be benign and even heroic. Xavier began as a grumpy martinet, but evolved into a kind, loving, self-sacrificing father figure to the entire X-Men universe.
The middling-to-poor movies were brilliantly cast (Patrick Stewart certainly looks the part), but they fell far short of capturing the true character of the team or the man.