Quantum entanglement is closely related with another quantum phenomenon that you might already know: the superposition principle. Let's say that I have a particle. My particle spins on itself. If I measure its spin, it can either spin to the left or to the right. I cannot know in advance whether it will spin to the left or to the right. And it's not just a lack of information because we can create an experiment in which the different spins of a single particle can interfere. We say that the particle's spin in a superposed state of both left and right, until we measure it.

Now there's already a good thought experiment that explains quantum entanglement: Schrödinger's cat. I have trapped a cat in a box, and I have installed a cruel setup inside. There's a detector in which I can enter my particle. If it spins to the right, the detector breaks a bottle of poison that kills the cat. If it spins to the left, nothing happens. Importantly, the detector does not communicate the measurement to me.

Now, I insert my superposed particle inside the detector and don't look at the result. The particle exits the detector and I can keep it. Because my particle was in a superposed state, I don't know wether the detector has measured a right or left spin. I don't know whether the cat is dead. Once again, it's not just a lack of knowledge because I could imagine an experiment in which its dead and alive state interfere.

Now imagine that I make a measurement of the particle's spin and it measures right. Then, I am 100% certain that the cat will be dead once I open the box. Even though both the particle and the cat were still in superposition, once I measure one, I will know the state of the other. That's quantum entanglement.

It's important because we can use this interaction between quantum objects to copy and paste information in a quantum computer without making a measurement. A measurement would damage the quantum information because it would collapse the superposed state.