rollup
A rollup is the most popular kind of layer 2: it executes transactions on its own faster chain, bundles many of them together, and "rolls them up" into a single compressed batch that it posts to the main blockchain. By doing the heavy computation off the base chain but anchoring the data and the final say to it, a rollup can run far cheaper and faster while still inheriting the base chain's security. This is the design most cited as the practical path through the scalability trilemma.
The crucial trick is that a rollup publishes enough transaction data on the base chain that anyone could, in principle, reconstruct and re-check the rollup's whole history. The base chain therefore guarantees that the data is available and unalterable, even though it never executes those transactions itself. Two families differ in how they convince the base chain the off-chain results are correct: optimistic rollups assume the batch is honest and allow a challenge period in which anyone can submit a fraud proof, while zk-rollups attach a cryptographic validity proof that mathematically demonstrates correctness up front.
Picture an accountant who does a month of bookkeeping on her own desk, then files one signed summary page with the official registry, while keeping every receipt available for audit. The registry does not redo her arithmetic, but it stores her summary permanently and can verify her work if challenged. That is a rollup: most of the labor happens off to the side, but the truth is nailed down on the chain everyone already trusts.
The two main families are optimistic rollups (cheaper to build, but withdrawals to the base chain wait out a challenge period) and zk-rollups (heavier math, but near-instant final proof).