Professor Xavier is the professor and head of the Xavier Institute, a home and training center for many of the X-Men that were once runaways or abandoned by their families. As he is an expert in mental health, continuing education standards of these runaways while helping them harness and control their mutant powers in an ethical way was the reason for establish the Xavier Institute. As a result, veteran X-Men have been supervised and trained at the facility, going on to battle villains and make the world a place in which mutants and humans can coexist. Some of these included Cyclops, Jean Grey, Rogue, Storm, Jubilee, Gambit, Beast, and Wolverine.
With extremely powerful telepath that can read minds, control others, and influence decisions by other people; as a long time scientist, he is also an expert in mental health. Continuing education standards in the Institute was his top priority, often staying behind while younger trainees were sent out to battle Magneto and other Sentinel robots. A large part of this reason is that professor X is a paraplegic, bound to a hovering "wheelchair". In the films, Professor X is portrayed by Patrick Stewart, which has an uncannily similar look to Professor X's original drawing that stayed consistent throughout the years.
As proponent of the development of mental health, continuing education for his mutant students was a large concern for the good professor. Often compared with Dr. Martin Luther King in personality and philosophy, Professor X attempted many different methods to find the underclass of mutants and offer his assistance in any way possible. While many turned him down for a life of crime or even to join up with Magneto, Professor X constantly used a telepathic device called Cerebro which allowed him to find the location of strays, dropouts, and undisciplined mutant youth around the world. After locating them, teams of X-Men would often approach them, offering a safe home for education and training at the Xavier Institute.
Beast, a professor and long-time friend of Professor X, often taught educational courses to new recruits at the Xavier Institute. Aside from this, Beast was also tasked by the professor to develop various technologies that would help young students harness and protect themselves from their often-unruly mutant powers that could cause harm to themselves or others. A good example of this was the development of a shielded gauntlet he invented for Surge, a young mutant who could not initially control large electronic blasts that she absorbed from various sources.
The Xavier Institute is extremely important to the X-Men series. Scenes often take place within the institute, either in the classrooms or training center, and were even featured as a setting in many of the films. Absolutely essential to the much of the settings of the X-Men Universe since the 1960s, the world of the X-Men we all love could never have been fully understood without the foundation of the Xavier Institute.