A fielder who is playing shallow or in is playing closer to home plate, while a player playing deep is playing farther from home plate than normal.
Regular terms are used for some positionings, for example, double play depth is used when there is a force play at second base. This means the shortstop and second baseman are playing slightly closer to second base and sometimes a little bit shallower. This position makes it easier to turn the double play. Bringing the corners in means the first and third baseman are both playing in, this will often be used with runners at third base.
Sometimes in the bottom half of the ninth inning (or later), when a team has a man on third base and less than two outs, the defending team will pull the outfields in very far, almost creating three extra infielders. This is sometimes known as do or die depth.
There are also some very irregular positionings. For example, versus excellent left-handed pull-hitters like Ted Williams, David Ortiz, and Barry Bonds, teams will move more players to the right side of the field. They sometimes play with the shortstop behind or even to the right of second base. The second baseman may simply move to the right, in which case this just qualifies as a shift, or he might move deeper into shallow right field—this particular formation is called the wishbone defense, because of the shape the shortstop, first baseman, second baseman, and right fielder make. This shift was in fact first employed against Ted Williams in the 1940s, as thought up by Indians manager Lou Boudreau, and may have significantly impacted his career average. "The shift", as it is commonly known, is also frequently used against other lefty sluggers such as Jim Thome and Jason Giambi.