Rollover (finance)
Encyclopedia
In foreign exchange trading (FX) a rollover is the action taking place at end of day, where all open positions with value date equals SPOT, will be rolled over to the next business day. This happens since in FX trading the trader doesn't want to actually buy the traded currencies but to continue to trade until position is closed.

For example, on Monday all position with value date of Wednesday (in case of T+1) will be rollover and the value date will be updated for Thursday. Position with value date of Friday will be updated with value date of next Monday.

Trading platform offer the rollover process but it involved rollover interest fee which is calculated according to the difference between the traded currencies interest rates. On the long position, the trader get the interest rate and on short position he needs to pay the interest rate. In case of weekends and holidays, the rollover is multiplied by the number of days of rollover.

Rollover is also a process whereby a financial instrument such as a CD is reinvested at maturity. It may also refer to the transfer of the balance of a 401k or IRA
Individual Retirement Account
An individual retirement arrangement is the blanket term for a form of retirement plan that provides tax advantages for retirement savings in the United States...

 into another 401k or IRA account (i.e. rolling over a conventional IRA into a Roth IRA
Roth IRA
A Roth IRA is a special type of retirement plan under US law that is generally not taxed, provided certain conditions are met. The tax law of the United States allows a tax reduction on a limited amount of saving for retirement. The Roth IRA is named for its chief legislative sponsor, Senator...

 or a 401k from a former employer into a conventional IRA).

When talking about payday loan
Payday loan
A payday loan is a small, short-term loan that is intended to cover a borrower's expenses until his or her next payday. The loans are also sometimes referred to as cash advances, though that term can also refer to cash provided against a prearranged line of credit such as a credit card...

s, a roll-over can be referred to as what happens when a borrower does not have enough money to pay back the loan when it is due. The borrower then borrows more money and the same rules apply (i.e. interest).
Sources:

thismatter.com/money/forex/rollovers.htm

http://www.dbfx.com/forex-trading/forex-rollovers
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