The basic push-up is perhaps the first exercise most kids learn. It's also one most adults can do even if they aren't putting in gym time. You can't do a proper push-up unless you have several major muscle groups working together, but it will most help those in the chest area.
The exercise targets the pectoralis major muscles and, more specifically, the muscles' sternal heads. People commonly refer to the pectorals as pecs or chest muscles, and the sternal heads make up the bulk of your chest. Strength in these muscles helps you accomplish a number of movements, including the internal rotation and extension of your shoulder.
ExRx.net notes that when you perform a push-up correctly, you're using three synergist muscles. The clavicular head of the pectoralis major, the anterior deltoid and the triceps brachii are found in your chest, shoulders and rear of your upper arms, respectively. In strength-training terms, a synergist muscle helps you accomplish the movement. For example, when you push yourself away from the floor, you work your triceps muscles.
This exercise also engages the rectus abdominis, obliques and quadriceps. Your abs and obliques are core muscles while your quadriceps are the large muscles in the front of each upper leg. These stabilizer muscles contract with little movement during the exercise. For example, you contact your abs and obliques to help keep your back straight during the push-up.
Execution of a push-up also requires the short head of your biceps brachii and erector spinae muscles. These muscles are found in the front of your upper arm and along your spine, respectively. During a push-up, your biceps are a dynamic stabilizer, while your erector spinae is an antagonist stabilizer. Both types of stabilizer help you execute the movement.