This official trailer sets up the game's single-player storyline. You're seeing bits of the game's missions in here.
Your reviewer plays two of the game's virtual training missions. This separate mode includes at least 22 platforming and combat challenges, each of them with a target score and an online leaderboard.
This is the game's multiplayer mode, as shown in a trailer at E3. The trailer doesn't show the actual gameplay perspective, which includes a radar that points in the general direction of the player's target. A portrait of their target appears on the upper-right of the screen. You'll have to spot them visually and not accidentally kill any of the numerous civilians who look just like them. After completing or failing that mission you are assigned another, until the session's time runs out. You get more points for kills that are done with stealth or acrobatics. Players who are doing well will find that they are hunted by more than one player.
This is a screen capture of just one of the many hidden Subject 16 puzzles in Brotherhood. As in Assassin's Creed II, someone else from modern times has managed to hide secret codes in the past of Renaissance Italy. By finding them, players access a sequence of puzzles that involve brain teasers, code-breaking, chess and more.