Recommending when to use and when not to use Illustrator involves a brief discussion about a couple of other programs in the Creative Suite: Photoshop and InDesign. Especially for new users, many of the tools and capabilities appear the same. They are, but there are both subtle and not-so-subtle differences between the programs that make differentiation necessary.
To explain this fully, let's talk about graphics first. There are two types of graphic formats: vector and bitmap. Vector graphics are created with curves and lines based on mathematical formulas. After you create a vector graphic, you can enlarge it, reduce it, or change it as much as necessary without having to worry about the graphic losing resolution.