For grip. When boots were first worn they were working boots and the studs were flat. Protruding studs made of wood were created and these were nailed into the shoe sole. These later were made of rubber moulding and later alluminium screw in versions. Studs were and are used to provide grip in grass and muddy conditions thus allowing plays greater maneuverability
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Football shoes have studs on them as studs make the lower part of shoes more rough and " the higher the roughness of a body the higher the friction will be when it interacts with other object". In this case the studs interact with grass or ground..
Cleated shoes provide traction against the playing surface, allowing the athletes to keep their footing. Without cleats, players would literally slip and fall all over the field. When field conditions become especially poor, you'll often see players switching to longer cleats for additional grip.
Footballers wear shoes with stud for the grip that is provided by the small area of stud.