Glossary
Merkle Tree
A binary tree of hashes that lets you commit to a large set of items in a single root and later prove any one item's inclusion with a tiny proof.
A Merkle tree hashes pairs of items, then pairs of those hashes, recursively, until a single root remains. The root commits to every leaf at once.
To prove that a given item is in the set, you only need the sibling hashes along the path from leaf to root — a "Merkle proof" — not the whole set. Block headers commit to all their transactions via a Merkle root, which is how light clients can verify inclusion without downloading entire blocks.