Time freezes and actors and things can be viewed from different angles. What is this special effect called and how is it made? [duplicate]

They use an array of cameras usually kept in curved setup having object in the middle. While every camera captures images from different angles, final shot is produced by editing frames from different cameras.

This technique is called Bullettime 360 Photography.

Note: This is an addendum to Rahul's answer, which is essentially correct.

In the Matrix movies, the filmmakers didn't rely exclusively on the still photos from the stationary cameras. To make the shot appear more fluid, they created many computer-generated still frames from angles that would appear to be between the positions of the stationary cameras. For example, the photo in Rahul's answer shows cameras that are about 12 inches apart; the shot would look much more smooth if the images were only an inch (or less) apart, so computer-generated images were created to simulate those angles. Of course they were completely photorealistic, and they used the still images taken by the cameras nearest them (to the left and right) to create the most realistic image.

As I said, this is true for the Matrix movies. I expect that it is true for other movies, videos, commercials, etc. that use the Bullettime 360 Photography technique.

I expect the music video is using a different technique than The Matrix.

The bullet time sequences in The Matrix are shot using an array of cameras placed around the actor.

I think the most likely way the effect in the music video was created, is to get the actors to stay still while the camera moves around them. 3D assets can then be placed into the scene to sell the effect:

There are multiple effects being referenced here. CSI season 10 opener did a variation of the freeze frame effect, which in that case was a combination of various methods:

http://nypost.com/2009/10/01/csi-freeze-frame

A video of the scene:

There is the matrix bullet time effect. The actor was suspended from wires and array of cameras used to shoot the scene. Then the video was cleaned up with computer assist and the green background replaced with the movie footage.

The 360 pan effect has also been done with computer generated graphics as seen at 0:22 into this video of McKayla Maroney's Olympic vault. The effect was used in other Olympic clips prior to this, but I couldn't find the older video. This one needs to be viewed via youtube:

Sport stations have been using the computer generated 360 events at football games and also at the 2017 US Open tennis championship. At the Dallas Cowboy stadium there is an array of cameras the the ends of the field and the computer apparently converts the images into internal 3d models to produce the effect. The main issue is the delay involved for the computer to generate a video sequence. In the case of the Dallas Cowboys, a system called FreeD is used. There's an example GIF on this web page:

https://www.sbnation.com/nfl/2013/9/8/4709234/sunday-night-football-360-degree-camera-shows-exactly-what-the