Its called cinematic camera.
Keys of note for vanilla minecraft:
F1: Removes the GUI from the screen. Great for those screen shots. Stuff like the hotbar will be completely gone until it is pressed again.
F2: Takes those screen shots
F3: Add lots of stats to the GUI. Very interesting. Can be paired with other keys for various different results. From reloading the chunk cache to crashing the game.
F5: Camera Placement. Toggles where the camera is in respect to the player.
F8: Cinematic Mode. Smooths and slows the camera movement in relation to input.
F11: Fullscreen/Windowed mode toggle
In case that information isn't fully accurate (which it never is),
This link is far more accurate and in depth (which you shouldn't follow BTW. Never trust random links on the internet. Especially in forums. Even if you recognize the site it is usually better to use your bookmarks to manually find the section of the site refereed to.)