Rollup
A layer 2 that executes transactions in bulk elsewhere and posts the results, plus enough data, back to the base chain.
A rollup takes many transactions, executes them off the base chain, compresses them, and publishes the compressed data together with a commitment to the new state, so that anyone can download the data and independently recompute what the rollup's state should be. Assets do not leave the base chain: they sit in a contract that records deposits and honors withdrawals once the rollup's state is proven or its challenge period passes. Rollups differ in how they establish that the posted state is correct, which splits them into optimistic designs backed by fraud proofs and validity designs backed by cryptographic proofs. Most run a single sequencer today and include an escape hatch that lets a user force a transaction in through the base chain if the operator censors or stops.
En pratique
Ethereum rollups publish their batch data in blobs and their state commitments in a base-chain contract, so a user can exit even if the rollup operator disappears.
Le malentendu courant
A rollup does not hand your assets to another chain's custody; they remain in a base-chain contract while the rollup keeps the accounting.