Entanglement is when two or more particles become connected in such a way that the state of one affects the state of the other, even when separated by vast distances. It's like a cosmic game of quantum telephone, where the information gets distorted, but the particles still somehow manage to be in sync.
But don't worry, it's not as weird as it sounds. Entanglement is actually pretty useful, allowing for things like quantum computing and quantum teleportation (just don't try that at home, folks).
Examples of Entanglement in Real Life or The Entanglement Paradox for more information.