The flush valve, a rubber component in the float system, covers the connection between the filler tank and the toilet bowl. When you flush a toilet, the handle attached to the swing arm or chain lifts the flush valve and allows water to flow from the tank into the bowl to flush water down the pipes. The flush valve wears out over time and needs to be replaced so the float can properly regulate the height of the water.
The swing arm in your toilet's filler tank is attached to the float ball and one of the most integral parts of the float system. If the arm rusts, bends or wears out, or one of the connectors to the main diaphragm ballcock is worn out, loose or broken, the arm will not swing properly with the float attached to the end of it. This can affect the level of water in your tank. All connections should be maintained and the float height adjusted according to the flush valve for proper tank maintenance.
The float ball is the most important aspect of the toilet float system, as it regulates the tank's water height. If the float is improperly adjusted, the tank will either underfill, in which case the toilet will not flush properly, or the water won't stop running because the tank will think it is never full. The float can be adjusted via the swing arm. You've achieved the proper height when the water valve shuts off the flow of water into the tank
Some float systems rely on a chain attached to the arm of the float to regulate the flush valve. If the chain wears out over time or one of the links breaks or slips off the connection to the swing arm, the toilet handle won't flush the toilet because the chain is no longer functioning. You can adjust the length of the chain along with the float to maintain proper water height in the tank.