Lightning payment channels are established by two parties Alice and Bob paying into a 2-of-2 multisignature address. Concurrently, they create two "exit-transactions", one for each participant which pay out the current allotment of the payment channel,
txBobExit_1. These exit transactions lock the fund of the executing party for some blocks.
When a payment is performed between Alice and Bob, they update the balance, create two new "exit-transactions",
To invalidate the previous "exit-transactions" each party gives the counterparty another transaction that builds on the previous exit transaction by spending the party's output to the counterparty if the old "exit-transaction" were broadcast to the network,
txBobExit_1-TakeAll. I.e. if Bob executes
txBobExit_1 the funds are time-locked for a little bit, meanwhile
txAliceExit_1-TakeAll would become valid and Alice could take them before he can spend them.