Time To First Page deals with the amount of time that it takes the printer to warm up and deliver the first page of a document. Even today, when printers essentially stay on permanently, they go into sleep mode when they are not being used to conserve power. As a result, when you use your printer for the first time after a certain period, the printer needs some time to wake up and prepare to print.
As you may guess, most printer manufacturers are not eager to include that time in their reports on how fast their printers are -- it would make their machines look a lot slower. As a result, when you see print speed reported in a manufacturer's spec list, the speed does not include the warm-up period.
With larger business machines, however, those times are important -- when you're spending several thousands of dollars on a printer or copier, you need to know how long it will take for that first page to emerge. And as smaller desktop printers started to enter the workplace, buyers wanted to know the same information about these desktop models.
For the most part, it doesn't mean a lot to those of us who print a few pages a day, and don't care if it takes an extra five or ten seconds for the printer to warm up. However, if you sometimes print in a hurry, or are simply curious about how much extra time it will take a sleeping printer to go into action, you may want to take note of the Time To First Page.

