A light wallet does not download the complete blockchain. Instead, it downloads the block headers only to validate the authenticity of the transactions. Because of this reason, light wallets are easy to maintain and run. Lightweight wallets use a method called Simрlifiеd рауmеnt vеrifiсаtiоn (SPV) to verify transactions.
Simрlifiеd рауmеnt vеrifiсаtiоn (SPV) is a method for verifying if particular transactions are included in a block without downloading the entire block.
See also this bitcoin wiki page