The basic idea
Classical computers process information as bits — values of either 0 or 1. Quantum computers use qubits, which can exist in a superposition of 0 and 1 simultaneously. This, combined with quantum entanglement and interference, allows certain calculations to be performed in a fundamentally different and potentially far faster way.
What quantum computers are good at
The advantage is not universal. Quantum computers excel at specific problem types: optimisation problems such as finding the best route through thousands of possibilities; simulation of molecular interactions for drug discovery; and cryptography — Shor's algorithm can factor large numbers exponentially faster than known classical algorithms, threatening current encryption. For running a spreadsheet or browsing the web, a quantum computer offers no advantage.
Where we are now
Current quantum computers are NISQ machines — Noisy Intermediate-Scale Quantum. They have enough qubits to do interesting things in controlled settings, but errors accumulate quickly and fault-tolerant quantum computation at scale remains years away. IBM, Google and a growing number of startups are racing to increase qubit count while reducing error rates.