Dictionary.com lists 42 definitions for this word, which can be an adjective, noun, or verb. So, I'm going to assume you know what double means...
Dating to the early 13th century, the origin of double is Old French doble ("double, two-fold; two-faced, deceitful"). Doble comes from Latin duplus ("twofold, twice as much"), which is a combination of duo + -plus ("two" + "more"). Duo derives from Proto-Indo-European *duwo, which is also the forebear of Proto-Germanic *twai, which became Old English twa (the feminine and neuter form of twegen). What is twa in Modern English? Two.
Surprised to see feminine and neuter in English? See my post on whilhom.