I wouldn't recommend reading the whole thing -- it's a manual. Read the introduction and maybe the "core" chapter. The intro is really short.

I don't have an example, but here are some motivations: Read it because you're generally interested in how people use programming languages to solve their problems. Read it because you use R and would like to have a really nice way of talking about array operations. Read it because you use APL and you want access to all of the neat stats functions R provides.