At my Czech university where I study computer science (but I believe math and physics are organized the same way here), most courses have both lectures (professor presenting the topic to a large class) and "seminars" (TA giving exercises and homework to a smaller class).
I believe courses at US universities have different structure and that the term "seminar" has different meaning. But there has to be something like our "seminars", right? What is it called? How does it look like?
This is often called a "recitation section".
Generally these are referred to as "labs" or "discussion" sections, as opposed to the "lecture" session.
Giving an example from computer science, it is not uncommon for there to be a lecture session where the instructor (such as the professor) talks about the material, takes questions, etc. Then there is often a lab session, often held in a computer lab, where students can work on hands-on assignments, homework, and course projects. These can be staffed by the instructor/professor or by student teaching assistants, or held as an open lab where the room is reserved but no one conducts the session - students come and go and work as they please.
In fields of communication, philosophy, and history, it is common that this lab session is replaced by a discussion session. The lecture is often of a mass variety, where the professor gives the talk to hundreds of students at a time. During the discussion session the professor or a student teaching assistant holds discussions, readings, gives out assignments, and various other similar tasks.
In physics and biology, again there is often a lecture or mass lecture held by the professor, then sometimes both lab and discussion sessions may be held. Again the staffing and locations vary, but the general theme is the same.
I have personally experienced these in a number of institutions in the US in the fields of biology, chemistry, physics, philosophy, history, communications, art, computer science, and psychology...so it certainly seems to be a very common pattern.
These non-lecture sections are almost always of a less-populated variety as well. If the class only has 20-30 students total, then the lab sections are of the same size. If the class is over 30, I have usually experienced lab and discussion sessions to be smaller, with as little as 12-20 students maximum - but this usually varies by room and lab availability and subject, and thus will vary by University, department, and subject.
In the Uk at least there are often tutorials which sound similar to what you describe. They consist of a small group of approx. 4-5 students with one tutor (generally a professor/lecturer/post-doc). The aim is to do exercises and go through problems the students are having with the course. Also you are often set homework for the tutorials.
I don't know how common this system is in other parts of the world.
As a variation on Bill Barth's answer, at my last institution, the local jargon was simply to refer to these class meetings as section.
I can't solve this homework problem, I'll ask my TA about it in section.
It may have been short for recitation section but I don't believe I ever heard the longer form.
At the institutions I've attended and taught at, these have been called "section" (I've never heard "recitation section"), "tutorial", "discussion section", "TA session"/"TA section", "lab", "small group", and "studio".
Of these "discussion section" was the most common and, at my BA and PhD institutions, the official title for it.
