A 'light client' is one of a couple of slightly different hacks, all that are intended to allow the user to have a local wallet.dat while not requiring the full blockchain.  The two big ways this works are 1) blockchain headers only client and 2) split wallet.dat client.  #1) Doesn't really save much bandwidth yet, because the network doesn't (yet) support partial block downloads so right now they have to download the whole block before discarding the parts it does not need, which is all of the transactions that do not include inputs or outputs that use any of it's own addresses.  However, #2 does work at present, and one wonderful such example is BitcoinSpinner for the Android smartphone OS.  How it works is that the phone keeps the addresses & their associated private keys encrypted on the phone, while the rest of what is kept in the normal wallet.dat file is kept on an account with the BitcoinSpinner server.  The server knows your (very few) addresses, and tracks your balances for you.  When you need to send money, your phone will inform the server to whom you need to send a transaction and for how much.  The server then creates the transaction based upon it's local blockchain & what part of the wallet.dat that it possesses, and then sends that to your phone which then uses the private keys to sign the transaction, and sends it back to the server, which then sends it to the network.  Method #1 was described in the original white paper by Satoshi, but method #2 seems to be the more practical method at this time.