What does "to pick someone's cherry" mean?
Nobody "picks" anybody's cherry. Cherries are "popped" and cherry in this case refers to hymen.
To "pop one's cherry" in a non-sexual way is to do a thing for the first time.
Cherry-picking is something else altogether.
From the New Oxford American Dictionary:
cherry (noun) 4. [in sing.] [vulgar, slang] the hymen, as representing a woman's virginity.