The fill valve (which used to commonly be called a ballcock) is a crucial part to water flow within a toilet. The fill valve is vital for bringing water into the toilet tank. This process of water intake occurs after the toilet is flushed. The sounds of water trickling after the flush cycle has happened is when the fill valve is refilling the inside of the tank. The fill valve interacts closely with the flapper, trip lever, and handle. Within the tank, the flush valve and flapper are attached to each other on one side, while the handle and fill valve are attached on another side.
The fill valve also plays another integral part in the toilet system— water maintenance. When another part of the toilet is broken (commonly the flapper or actuator) the fill valve will automatically turn on in order to keep the water at a safe level within the tank. If your toilet sounds like it is constantly running, it likely means a part within the tank is broken, and the fill valve is in a constant cycle of staying activated to ensure water levels stay the same.