An extension payment is a payment a taxpayer makes with a Federal or State extension instead of a tax return.
If you don't think you will be able to file your return on time (April 18th this year), then you can file an extension to get 6 more months to file your return. However, an extension only extends the amount of time for you to file your return, it does not give you more time to pay your taxes due. So, while an extension will protect you from penalties related to not filing a return on time, any interest on taxes due will continue to accrue. This is why some people choose to make a payment of taxes when the file an extension - to reduce any interest owed. This is called an extension payment and the program may ask you during filing if you made any such payments so the program can correctly reduce the amount of taxes you owe by the payment already made.
@Nara268 Its ok if you can't make a payment - it just means you will wind up owing more interest overall (and a good percentage of people actually don't make payments when they file extensions so its not uncommon at all). But, even if you can't make a payment, the important thing is that you still file an extension. Because the penalty that is severe is the failure to file penalty and the extension will protect you from that penalty.