You might know it as calisthenics, bodyweight training, body weight resistance exercise, TRX Suspension Training, gymnastics rings, sling training, straps training, rope work, hand- or foot-suspended strength exercises.
At its most basic, this type of strength workout involves the primal movements we’ve been making since we ventured out of trees. On the other hand (or paw, as the case may be) a movement like the pull-up vastly predates bipedalism and modern human anatomy!
For concrete examples like push-ups, inverted rows, or dips, see examples here or the principles of progression here.