An optimistic rollup posts a state root to Layer 1 with no proof of correctness. The state is "optimistically" assumed valid. Anyone can challenge the state by submitting a fraud proof during a window (typically 7 days). If a fraud is proven, the state is rolled back. If no challenge succeeds in the window, the state is finalized.
When a user submits a transaction, the rollup sequencer orders it, executes it, and includes it in a batch posted to L1. The sequencer is trusted for ordering but not for correctness; if it tries to cheat (post an invalid state), any honest party with the rollup data can submit a fraud proof. Fraud proofs work by replaying the disputed transaction on L1 and showing the result differs from what was claimed.
The 7-day challenge window means withdrawals from the rollup to L1 take 7 days unless you use a third-party "fast bridge" that fronts the funds and accepts the delay. Major optimistic rollups: Arbitrum, Optimism, Base.
Optimistic rollups dominated rollup adoption first because they are simpler to build. The 7-day withdrawal delay is the main user-experience friction; ZK rollups solve this at the cost of much harder cryptography.
Base (the L2 TerminalFeed accepts USDC payments on) is an optimistic rollup. The 7-day challenge window does not affect deposits to TerminalFeed; only withdrawals back to Ethereum L1 face the delay.