The PhD student seminars are intended to be informal and relaxed without the "polish" of the official seminars. The seminars can discuss for example recent results (your own or from an article) or survey some interesting topic. The intended audience is primarily PhD students, but everyone is welcome. Contact Kilian Risse if you want to give a seminar or receive email announcements about upcoming seminars.
See also the page with the TCS groups official seminars.