Illustrator is a wonderful piece of kit that has amazing vector editor functions. It can be used to create incredible illustrative artwork, corporate logos, page layouts, website, print designs, and vectors for literally just about anything with which you might need a vector. Images with Illustrator are vector based so it can be scaled to any size without losing quality.
Graphic Design is a field like very few that attracts many sorts of people from many sorts of backgrounds. Common to misconception is that graphic designers come from an arts background or needed to have taken a degree in graphic design at university. Much more to the truth is that universities are in fact not nearly as popular as they once were for anyone thinking of studying graphic design as not only is arguably an unnecessary expense but there are many courses and alternative ways of studying.