Yes, just as you technically can watch a 3D movie with both eyes open, but also:
No, not unless you switch your hand back and forth between your eyes REALLY fast (like, at least, 60 times a second), or blink that fast.

If you cover one eye, and have the other one open, you'll still see the two different images, flickering between them. It will basically look blurry. The key point is that the glasses switches back and forth between the eyes, in sync with the projector/TV switching the two images.

It's basically this effect: https://i.stack.imgur.com/CGbUh.gif, but much faster (and a video, with moving subjects, etc)

Besides polarization (like mentioned in other answers) there is another technique (albeit it might not be as commonly used today): Active Shutter 3D system.

These glasses is, usually, a lot bigger, and needs batteries. They work by blocking one eye (like an eye patch), and then quickly switching to the other eye. The glasses do this really quickly. And at the same time the projector (or TV) shows one image for say the right eye, and then quickly changes to an image for the left eye. The TV/projector sends a signal to the glasses so the glasses switches eye at the same time as the TV/projector.

The difference between the two images is that one taken a little to the side to the other. Where the right image might show a little more of the right side of an object, and vice versa, this gives a perspective effect. And since this is how our eyes work, and how we perceive depth, you perceive the things on screen to have a depth to them.