Essentially another term for pre-paid, meaning service that is paid in advance, as-needed, instead of billed at the end of each month (post-paid). Since service is paid for in advance, there is no generally no need for contracts or credit checks with pay-as-you-go.
One difference from prepaid is that a PAYG plan can (optionally, usually) be set up to automatically deduct funds from a bank account when depleted, instead of the balance simply becoming zero, rendering the phone unusable until the account is manually replenished.