To avoid all confusion from the start, “Kaffee (= coffee)” is a very serious topic. “Kaffee” is more than a plain beverage. Kaffee is more than some warm / hot, brownish, caffeinated liquid in a paper cup. “Kaffee” is more than a conversation topic between supporters and opponents of fair trade. “Kaffee” is more than the smuggling good many usually proper German citizens tried to sneak in from Belgium or Luxembourg before the European Single Market was established. “Kaffee” is a meal.
“Kaffee”, while the word actually refers to nothing but the beans, the powder or the beverage, has been used as the generic term for a meal held somewhere around 3pm to 4pm. Savoury items are usually not served at “Kaffee”. Instead, your host will likely treat you to a variety of sweet pastries in addition to coffee as the main beverage. It’s perfectly normal to get invited to a birthday “Kaffee” on the Sunday following the actual birthday; light snacks and dinner unspokenly follow.
Beware though not to bring a cake of your own unless you get explicitly asked to do just that (which usually only is the case at large informal family gatherings or some kind of fundraising cake sales at school carnivals). You might imply that the host is not able to feed you properly (i.e. to stuff you to the brim until whipped cream starts oozing out of your nostrils. “You’re welcome!” on the visual.) If somebody invites you for “Kaffee” and offers you only just that and not even a few store-bought cookies, that person hates you. If it’s a prospective mother-in-law, then she hates you with a passion. Germans love pastries (a post on pastries in particular is soon to come), and while there seems to be a bakery on every other corner, many pride themselves in their homemade pastries. Above you see a sample I contributed to a family gathering “Kaffee”. I did a close-up so you will neither have to see my family nor too much of the emergency-1970s-garden-chair cushion. Alas, people had already started eating of it (the cake, that is) before I could snap the picture, but I hope you’ll get an idea nonetheless.
Finally, a note on “Kaffee” as a beverage: in comparison to the US, coffee is usually much stronger in Germany. There are people like me who enjoy their coffee particularly strong. As my father puts it, my coffee bears the eschatological message that resurrection from death is possible.