The Keurig is a wonderful invention, and they thought ahead. There is a reservoir beneath the (removable) grate where you put your coffee mug. Seems they knew that stupid people like me would occasionally forget to put a mug underneath to catch the coffee (or tea, if that is your preference), and without a hollow place to catch the coffee, there would be a horrendous mess.
I've forgotten three times.
Though I did realize it in time to whip my mug underneath, so that no more than half of it was wasted. My brother tells me now, "Don't forget your mug~ If you forget again, I will laugh without shame at your expense." Thanks, bro. I know where you sleep.