Definition
A quorum is the minimum number of replicas that must participate in a read or write for it to count as successful. With N replicas, a write requiring W acknowledgments and a read consulting R replicas guarantee that a read sees the latest acknowledged write whenever R + W > N — because any read set must then overlap any write set in at least one replica.
With N=3 and W=2, a read quorum of R=2 gives 2+2=4 > 3: every read touches at least one replica holding the newest write. R=1 could hit exactly the replica the write skipped. Tuning R and W trades latency and availability against staleness — W=1 makes writes fast but weakens the guarantee; W=N makes writes durable-everywhere but fragile. This is the tunable-consistency model behind Dynamo-style stores such as Cassandra.
How it comes up in interviews
The overlap argument is the whole point — interviewers ask "N=3, W=2: what R guarantees reading your own write?" to check you can reason it out rather than recite it. Follow-ups probe what happens when a quorum is unreachable (unavailability vs sloppy quorums with hinted handoff).