https://www.youtube.com/watch?v=-d4NAEPZrbg
To a layman like me, the most interesting bits start at: 6:14 and 37:36. If you're interested in the materials (they're perovskite crystals) it's at 22:45.
My explanation as a total layman: There are materials that when you apply an electric field to them they almost immediately heat up. Then as you keep the field on them they cool down again naturally, and if you then remove the electric field they cool down quickly. So you with electric fields you can make the material do a pretty wild temperature swing.
Then the next trick is to extract that temperature differential from the device. You could imagine a container with a fluid and the device in the middle, a hot side on the right and a cold side on the left. As you push fluid to the right you heat up the device, and as you push fluid to the left you cool down the device. This will over time sort of ratchet the both sides to greater extremes. Even simpler they also made a "slapper" which simply puts the device on a little motor actuated arm, and it slaps the device to a load whenever its cool, and then to another load when it's hot.
Other (to me) cool detail is that they got Murata to manufacture these devices as MLC's, so it's just your typical Murata MLC capacitors but with these electrocaloric material layers.
edit: also at 44:00 he shows a slide comparing this technology to others, and it shows that even though it's more efficient than vapor compression it's less efficient than acoustic, although they're both very efficient. So I guess the big question is going to be is if this is going to be more practical/economical. From what I've heard there's a bunch of companies already moving forward with manufacturing thermo acoustic heat pumps so those are definitely further along.