A gymnasium where you can work out, alternate between sauna, hot tub and swimming pool, etc. Not necessarily a commercial enterprise; the YMCA and JCC are good examples of nonprofit organizations known for their health clubs.

A health club is more than just a gym, IMHO. I really do believe it is exactly what it advertises; it's a club people can join to improve their overall health, not just get sweaty. This of course includes things like stationary bikes and treadmills and the usual torture devices, but it's also a place to relax, play sports and even get a massage or advice about nutrition. Any health club worth its salt will also have a childcare facility of some sort.