Antarctica is full of glaciers and some excursions venture into areas where crevasses are present. For safety, you'll rope up and use crampons when traveling in these areas. Generally no prior experience is necessary to participate and most of the specialty equipment needed will be supplied.
In terms of physical fitness you’re going to want to be in good enough shape that you’re up to the task of walking for four or more hours over fairly rugged terrain that includes hills. Guides on most vessels reserve the right to refuse somebody a spot on a mountaineering trek if there are concerns about their health.