In Olympic-style team figure skating , the “events” are really the four standard figure skating disciplines, each skated in (at least) a short program and a free skate:

  1. Men’s singles
  2. Women’s singles
  3. Pairs
  4. Ice dance

In the team event, every country enters:

  • One men’s singles skater (or pair of skaters, for pairs/ice dance) for the short program in each discipline.
  • Then, after a cut, one entry per discipline again for the free skate/free dance.

A simple way to picture it: it’s the same kinds of programs you see in the individual competition (men, women, pairs, ice dance; short and free), but the results are converted into points for the country instead of medals for just the skater.