They're built off fundamentally different basic units. Contemporary computers use transistors, which occupy traditional physics and do logic with voltage thresholds. Quantum computers use a quantum phenomenon -- one easy-to-understand (and fairly easy to construct) quantum computer substrate uses the spin of electrons in superconducting loops. Electron spin is a quantum phenomenon, in that the spin isn't deterministically positive or negative, it's a probability distribution -- initially, equally likely to be positive or negative, but you can't tell what it is until you actually read it. It's not 0.0, it's either -0.5 or 0.5, both with a 50% chance. Equally importantly, you can perform (physical) operations on electrons singly or in pairs in order to manipulate these probabilities. Quantum computing is turning these probability fields and operations into useful computational results.