In regular computers, you have bits. To process that information, every bit is essentially represented as a wire. You need 8 bit-wires to represent a byte, and each bit-wire either has current or it does not -- it's either on or off, either 1 or 0.

In a quantum computer, information is stored as quantum wave states which can stack on top of each other in a single wire. A q-bit (quantum bit) shares space with potentially hundreds or thousands of other q-bits. You only need one wire to process them all simultaneously. Each wire might have a thousand 'on' q-bits and another thousand 'off' q-bits, and the quantum computer can keep track of them all. So you see that a quantum computer theoretically processes at ENORMOUSLY OMG FASTER speeds than a regular computer.

Quantum computing has nothing to do with entanglement. Entanglement is something else that's mostly theory, while quantum computing is real and being developed now.