The dictionary says it's an informal social gathering for coffee and conversation ... and that's a pretty good definition!
At Eastercon, if there are kaffeeklatsches (or "klatches" for short) then they are a chance for around eight-to-ten people to sit down with a guest and have a cup of tea/coffee/whatever and just chat.
The usual structure is that a list of klatch sessions will be posted up somewhere with the name of the guest, the day/time of the klatch and eight to ten blank lines underneath. You fill in your name to say you want to attend a klatch (as long as there's a free line left!)
At the appointed day/time you show up at the location (often a room near the bar!) and, depending on the convention, you may have to buy your own tea/coffee. After that it's left between the group of you and the guest what you talk about for the duration of the klatch.
For particularly popular guests, it is common to have a much longer sign-up sheet and then to do a random selection of names from that sheet to select the eight or ten people to chat with the guest.