Two bits is a quarter of any given denomination.
Piece(s) of eight, times two = Two Bits.
Historically, coins such as Spanish silver reales, were divided into eighths for small purchases.
Today our base denomination in these united states is the dollar.
A bit, or one eighth of a dollar is 12.5 cents.
Two bits is a quarter dollar, or in older times, 2/8 oz of silver.
The term "two bits" is applicable to any currency, but since abandoning gold and silver, somewhat antiquated and irrelevant, since no one really cuts up coins anymore.
edit - punktyouashun