From YPPedia

A ship in the battle nav portion of a sea battle has the option to place a grapple token along with each regular move. Unlike firing the cannons, throwing a grapple does not use any of the ship's resources. Like firing a cannon, a grapple may be thrown off either the left or the right side (but not both at once). If a grapple is selected, cannons may not be fired on that phase of the turn. If an enemy ship is in the square adjacent to the side of the ship that the grapple is thrown off of, it is considered "grappled". When this happens, the swordfighting or rumble portion of the sea battle begins.

Unlike moving or firing a cannon, placing a grapple does not affect the status bar above a ship during a sea battle. Thus, a ship can have four grapples placed, and as long as it is not moving or firing during that turn, appear as though it is taking no action that turn. This commonly occurs when a brigand has run out of moves.

The grapple tokens are disabled during blockade navigation, as you are not allowed to board other ships in the blockade zone.

Historical Note

Prior to release 2004-04-28, grapples did not exist. The swordfight or rumble began when both ships occupied the same square on the battle navigation board. (There was no such thing as ramming at this time.)