Simplified Payment Verification (SPV) software enables one to verify one's own blockchain transactions without verifying anyone else's, thereby requiring only 'lightweight' software, made possible by a Merkle tree hash structure.
The software run by SVP (or 'lightweight') wallets performs different, simpler operations than the full verification payment (FVP) software run by full nodes (or 'heavyweight' wallets).
Full nodes verify transactions by downloading and examining the entire blockchain until the transaction's origin is found and then comparing results with other nodes until a consensus is reached. In contrast, SVP wallets need only to check that full nodes have validated the transaction and that the transaction has been added to the blockchain. To do so, they employ a hash structure known as Merkle tree, which only downloads block headers instead of full blocks. SVP software is attractive because it allows one to verify one's own transactions without verifying those of anyone else.