Optimistic Rollup
A rollup that assumes posted results are correct and gives observers a window in which to challenge them with a fraud proof.
The operator posts a new state commitment without any proof that it is right, and the base-chain contract accepts it unless someone submits a fraud proof before a challenge window closes, commonly about seven days. If a challenge succeeds, the incorrect commitment is discarded and the party that posted it loses its bond. This is why withdrawals to the base chain wait for the window to pass, unless a third party fronts the funds immediately for a fee and takes the delayed withdrawal itself. The security of the design rests on at least one honest, funded party being able to watch and challenge, so restrictions such as a permissioned challenger set are a meaningful limitation rather than a detail. Arbitrum and Optimism are the best-known implementations.
In practice
A user withdrawing from an optimistic rollup either waits out the challenge period or pays a liquidity provider to receive base-chain funds immediately.
The common misunderstanding
The withdrawal delay is not congestion or slow processing; it is the challenge window that the security model requires in order to work at all.