When muscles get bigger, it is called hypertrophy. The size of your calf muscles might be dictated somewhat by the length of your Achilles tendon – if you have a short Achilles tendon, your calf muscle will be much bigger, but if you have a long Achilles tendon, then the calf muscle will be much shorter, so this could be one reason it doesn’t look very big.
To make a muscle grow bigger and stronger, you need to make sure you target it in training. Your calf muscles (gastrocnemius and soleus) are very important in everyday life as we walk from place to place, so they are very used to low-intensity work. To target the calf muscles, you need to do exercises that involve you going up on your tippy toes, so you could do this type of exercise over the edge of a stairs step for example. Some people then hold extra weights to make it more difficult. Doing squats can help too, as gastrocnemius has been shown to work hard during this type of task too as not only does it help you push off the ground with your toes, but it also stabilises your knee (it is a biarticular muscle, meaning it crosses two joints).
Making sure you don’t overdo it exercising the same muscles every day, and making sure you get sufficient food for recovery is also important to make sure your muscles grow bigger. Also worth remembering that even though the muscle will get stronger almost straightaway with training, it will take several weeks to see a difference in their size. It takes muscles a while to grow.
The exercises you are doing may not be targeting specifically the gastrocnemius. Laura Anne has provided some good examples of exercises that can be used. It is important to not just focus on one muscle though and focus on the body as a whole. For example, if working on strengthening your back muscles you also need to strength your chest and core to ensure all muscles are working together and you are not weakening the opposing muscle groups.