What is the use of First() and Follow() in compiler design?
$FIRST$ and $FOLLOW$ sets are used by the algorithm which produces an $LL(k)$ parser from a grammar. They're also used in a number of other algorithms which analyze grammars, but most students will run into them when learning about top-down parsers.

Parsing is a tiny part of the work of producing a compiler, and in practice you can generate a parser using code-generation tools which avoid you having to know much about implementation details. So I'd say that th4e direct answer to your question is that $FIRST$ and $FOLLOW$ sets have very little to do with compiler design, but they are useful in the understanding of how particular parsing algorithms work.