Literally, it means "is", but it's probably best to simply treat it as a word which grammar requires in this sort of present-tense sentence with a noun as object.
(A bit like "does" in "Does the bird sing?" -- it doesn't actually mean anything, but you need it to make a grammatically correct question in English, since we don't say "Sings the bird?" anymore.)
Word for word, you could translate Mae Owen yn hoffi pannas as "Is Owen in liking parsnips" but it's best, I think, to just learn that this is the way to say "Owen likes parsnips" in Welsh.
Btw, such words have a name - https://en.wikipedia.org/wiki/Copula_(linguistics)