Properly, it should be spelled béguine, but it's been anglicized. It was made briefly internationally popular by Cole Porter's 1935 song "Begin the Beguine":
When they begin the beguine,
It brings back the sound of music so tender
It brings back the night of tropical splendor,
It brings back a memory ever green.
(Note the rhyme with green.) At the time, in French, béguin(e) meant a crush, both the feeling and the person crushed upon, but originally meant a nun's hairstyle or headdress, derived from the Beguine order of nuns, which had slightly laxer rules than some orders in that members could leave to marry instead of staying for life, which was named after their medieval founder, a priest from Leige known as Lambert le Bègue, meaning Lambert the Stammerer. Their male counterparts were a mendicant order, the Beghards, from which we get beg and beggar.
And if that isn't enough shifting meanings over history to satisfy you, I got nothin'.