Teleportation is pretty firmly situated in the realm of science fiction. We may not be able to teleport objects or people from place to place in an instant, but there are scenarios where teleportation can be achieved. Not only is it possible, but it's actually being accomplished in physics labs across the world.
Of course, we have to be careful about what exactly we mean when we say "teleportation." There's three different kinds of teleportation: teleportation through a wormhole, or something similar, where your body is simply relocated to another place; the Star Trek kind where your molecules are disassembled, beamed somewhere else, and reassembled in the same way; and the philosophy problem kind where your body is scanned and the information is transmitted somewhere else and used to build an entirely new body out of different materials. We're talking about the last kind here.
It turns out that that scan-and-reassemble type of teleportation is actually possible thanks to a property of quantum mechanics called "quantum entanglement." Quantum entanglement occurs when two or more particles are forced to hold mutually exclusive states, so determining one simultaneously determines the other.
Think of it like ordering takeout at a fast food joint. If you order both a burger and a grilled chicken sandwich, you don't know which is which before opening the boxes. But as soon as you open one, you immediately know what's in the other without looking. This is true regardless of how far away the second box is.
The same is true of quantum particles. If you have two entangled particles, knowing the state of one will automatically tell you the state of the other as well. And just like with our fast food, this is independent of distance, which means we can use entanglement as our teleportation method.
From here, the rest is simple. If we take two particles, entangle them, and send one to the moon, then we can use that property of entanglement to teleport something between them. If we have an object we want to teleport, all we have to do is include that object in the entanglement. The actual process to do that does require a bit of math and some careful setup and observations, which walks through in the video above.
After that, it's just a matter of making an observation of the object you want to teleport, which sends that information to the other entangled particle on the moon. Just like that, your object is teleported, assuming you have enough raw material on the other side.
Of course, teleporting large objects or people is probably not going to happen anytime soon. Keeping particles entangled for a long period of time, over long distances, or along with objects larger than a few atoms is way beyond what current technology is capable of. However, this experiment has been performed multiple times with small particles, and scientists have managed to teleport various electrons, photons, and even entire molecules dozens of miles. Perhaps this same tech will be used to send you or your grandchildren to the moon someday.