Closing out means buying an option you sold, or
selling an option you bought — essentially canceling out
your open position.
If you're an options holder you might close
out your position by selling the option, rather than exercising
it. If the premium
has gone up since you bought it, closing out could mean making
a profit. If the premium has decreased, closing out would mean
cutting your losses, and offsetting at least part of what you
paid.
Since you can close out your position, or buy
back an option you sold, as an options writer you're almost
never forced to fulfill an obligation to buy or sell the underlying
instrument — assuming you close out before the option is
exercised. Depending on the option's premium when you want
to buy it back, you might pay less than you received, making a
net profit. But there's a chance you'll have to pay
more than you received, taking a net loss. If that loss is less
than what you would have faced if the option had been exercised,
closing out might be the best exit.