Take two qubits and entangle them. Now neither one has a state of its own. Only the pair has a state.
Measure one and you get a random result. Measure the other and you get a result that is correlated with the first - perfectly, every time, no matter how far apart they are.
The usual next sentence is "so information travels instantly." It does not. You cannot control what your measurement gives you, so you cannot send anything. Two people holding entangled qubits each see pure noise. Only when they compare notes afterward, over an ordinary channel, does the correlation show up.
For computing, the point is that entanglement lets a set of qubits represent correlations that separate qubits cannot. Describing n entangled qubits classically takes an amount of bookkeeping that doubles with every qubit you add. That gap is where the potential advantage lives.