Pídeme means "ask me" or "request from me." It's a command form of the verb pedir (to ask for, to request), combined with the pronoun me (me).
In this song, Diego Verdaguer uses Pídeme repeatedly to set up a series of impossible requests, like touching the sun or counting desert sands. He then contrasts these with the one thing he cannot be asked to do: stop loving his beloved. This word is central to the song's theme, highlighting the depth of his devotion and the limits of what he's willing to sacrifice.