An option is a contract that gives the buyer the right, but not the obligation, to buy or sell an underlying asset at a specific price on or before a certain date. An option, just like a stock or bond, is a security. It is also a binding contract with strictly defined terms and properties. The vast majority of options are either American or European options.
An option can only be exercised before the expiry date if it's an American-style option. European-style options can only be exercised on the expiry date (somewhat more like futures in that respect).