The Mensa is the university's canteen, open to both students and staff. The food here is subsidised and therefore very low-priced.
The Mensa building is situated on a little hill just above the MPI-INF (D4.1
on the campus 
map). The building has quite a remarkable design of coloured concrete (seems rather strange today, but it won an architecture prize in the sixties), so you can't miss it.
The mensa offers lunch from Mondays to Fridays.
In the mensa café on the ground floor you can have breakfast and lunch from Mondays to Fridays. During the semester, they also serve dinner.
There are different categories of food: set meal (regular, non-vegetarian, complete set meal with soup/salad, main course and dessert), vegetarian meal (no meat or fish, complete set meal with soup/salad, main course and dessert), free flow (single courses from which you can assemble your lunch, slightly more expensive than the other categories), Tellergericht (one plate with a main course and a side dish, very low priced), and Salatbuffet (salad buffet; you pay by weight).
You can find the opening hours and the menu (updated weekly) on the website of the Studentenwerk.
You need your student identity card, that you can charge with money at machines on the ground floor and upstairs, for paying at the Mensa.
There are several other cafés and restaurants on campus, e.g. AC (Ausländercafé), Canossa, Juristencafé, Schlemmereule, etc.
Check their menus online.