Crisis Core begins seven years before the events of Final Fantasy VII, and many characters from that game and other related works appear. However, the primary characters in the game are from either SOLDIER (the Mako enhanced superhuman soldiers made by Shinra to work for them), or from their covert branch of operatives, the Turks.
Crisis Core is an action role-playing game in which the player controls Zack Fair. The player moves Zack through and between open areas, allowing him to talk with non-player characters, interact with the environment, and engage monsters in battle. At save points, the player may opt to take one of the available side missions, and if so, Zack is moved to a special area to complete the mission, which usually involves defeating one or more monsters. If the mission is successfully completed, the player is rewarded with beneficial items, and often new missions become available. Whether the player is successful in the side mission or not, upon completion, Zack is returned to the save point in the main game.
Source: Wikipedia, "Crisis_Core:_Final_Fantasy_VII," available under the CC-BY-SA License.