Often times a compiler works a lot with trees. The source code is parsed into a syntax tree. That tree might then be transformed into another tree with type annotations to perform type checking. Now you might convert that tree into a tree only containing core language elements (converting syntactic sugar-like notations into an unsugared form). Now you might perform various optimizations that are basically transformations on the tree. After that you would probably create a tree in some normal form and then iterate over that tree to create the target (assembly) code.
Functional language have features like pattern-matching and good support for efficient recursion, which make it easy to work with trees, so that’s why they’re generally considered good languages for writing compilers.