How Does a Merkle Proof Allow a Light Client to Verify a Transaction?

A Merkle Proof provides the minimal set of hashes required to verify that a specific transaction is included in a block, without downloading the entire block. A light client only needs the Merkle Root of the block and the proof (a branch of hashes from the transaction up to the root) to confirm the transaction's existence.

The client re-computes the path and checks if the final hash matches the known Merkle Root.