What is a light client (SPV)?

A full node downloads and checks every block and payment. A light client keeps only the block headers, 80 bytes each, and asks servers for a proof that a payment sits in a block. That is cheap enough for a phone.

Simplified payment verification, SPV, comes from section 8 of the Bitcoin white paper. A light client knows a payment is buried under real proof of workProof of workA puzzle that takes a computer real effort to solve, so the answer proves the effort was spent. Bitcoin’s miners use it to add each block., but it cannot check every rule itself, so it trusts that miners are following them.

Many mobile wallets are light clients. Some use compact block filters (BIP-158), which let them find their payments without telling a server their addresses.