Simple Payment Verification (SPV) is a technique described in Satoshi Nakamoto's paper. SPV allows a lightweight client to verify that a transaction is included in the Bitcoin blockchain, without downloading the entire blockchain. The SPV client only needs download the block headers, which are much smaller than the full blocks. To verify that a transaction is in a block, a SPV client requests a proof of inclusion, in the form of a Merkle branch.
SPV clients offer more security than web wallets, because they do not need to trust the servers with the information they send.