Brace is a line running from the end of a yard, in pairs, i.e. port and starboard braces, usually led aft to the deck. Braces for a mizzen may run forward as there isn't enough deck length aft of the mizzen to run them. The main mast, if there isn't enough room, may run from the yard to the mizzen mast then down the mizzen to the deck.
The purpose of the braces are to set the angle of the sail to the deck depending the direction of sailing according to the wind.
Brace at Wikipedia.