For gym novices, push-ups can provide enough of a muscle stimulus to grow, especially if reps, sets and tempo are progressed over time.
Once a certain level of strength and size is attained, however, this stimulus may not be sufficient for further gains. Push-ups will therefore need to be used as part of a progressive resistance training program. They can be used as "primers" as part of a warm-up, or "finishers" to help build a pump at the end of a lifting session.