Sidechain
An independent blockchain with its own validators that connects to a main chain through a bridge.
A sidechain runs its own consensus and produces its own blocks, so its safety depends on its own validator set rather than on the chain it is associated with. Assets move across by locking or burning on one side and issuing a representation on the other, which means the bridge contract and its key holders are part of the security model. If the sidechain's validators collude or its bridge is compromised, users can lose funds while the main chain continues operating perfectly, because the main chain never verified anything the sidechain did. Polygon's proof-of-stake chain operated in this shape, periodically writing checkpoints to Ethereum, and the checkpointing does not by itself let Ethereum reject an invalid sidechain state.
In practice
A sidechain can be faster and cheaper than the chain it connects to precisely because a smaller validator set is producing its blocks.
The common misunderstanding
A sidechain is not secured by the chain it connects to; its safety rests on its own validators and on the bridge that links them.