The question is simple: why are some functions called 'forms'? Modular 'forms', bilinear 'forms', differential 'forms', quadratic 'forms', and so forth. It is not concretely a mathematical question but I suppose the origin of the term must be mathematical, so I ask it here.
Thanks for the comment, it seems the question was already answered here: What do mathematicians mean when they say "form"?
and here's another page: Earliest use of the word "form" in mathematics?