From BR Bullpen

The backstop is the low barrier which marks the end of the section of foul territory behind home plate that is in play. It is usually a semi-circular wall topped by a high mesh screen, with the first row of seats located immediately behind the screen. The distance between home plate and the backstop, and the amount of foul territory behind home plate, varies from ballpark to ballpark. The further the backstop is from the plate, the more the park favors pitchers, as it means that a greater number of foul pop-ups hit behind home plate will be in play and potentially catchable.

In the early days of baseball, there was no backstop, and balls not caught by the catcher could roll a considerable distance, although there were often spectators standing behind home plate acting as a human backstop. A ball that hits the backstop remains in play, like a ball that hits the the outfield fence. A wild pitch that is thrown particularly hard can bounce off the backstop right back to the catcher if it strikes it at the right angle, allowing the catcher to tag out or throw out any adventurous baserunner trying to advance.

The catcher is sometimes also called the "backstop".