What on earth are these 'PaymentIDs' I keep hearing about?

The way that Monero works today causes the exchanges to have a single address to where all customers' moneroj get deposited. Given the intrinsic privacy features built into Monero, the exchange is unable to verify the source of any incoming transaction. Enter 'PaymentIDs'. Each exchange user get's a unique PaymentID assigned, so that by tracking PaymentIDs on incoming transactions, the exchanges can identify the user account that is to be credited.