Eating more protein in and of itself will NOT make muscles bigger. In order for muscles to grow, they must be subjected to physical activity, mainly resistance training. One can use weights such as barbells and or dumbbells and or a combination of exercise with weights and their own body weight (pushups, pull-ups, etc.). When muscles are subjected to these types of exercises, small, but significant changes begin to occur. The exercises create reversible "damage" to muscle tissue. This damage requires healing, and the healing that occurs requires specific nutrients, the main one being nitrogen-rich protein.
During the healing process, protein synthesis occurs within the muscle tissue, resulting in stronger and bigger muscle fibers than what existed before the training and healing process. Since protein is the only nutrient to contain significant amounts of nitrogen as part of its component amino acids, it is the only nutrient that can help stimulate muscle growth. Nutrients such as vitamins, minerals and other cofactors also play a role in building muscle, but this is a more “supporting" role than "leading “role.
To achieve maximum muscle building results from training, a well-balanced diet consisting of high-fiber complex carbohydrates, healthy fats (nuts, seeds, olives, avocado, etc.) and lean proteins (chicken, fish, lean meat) as well as protein supplements such as found in protein shakes (provide a convenient source of protein) will help one achieve the results they seek when it comes to growth of muscle.