When one server can't handle all your users, you add more, and a load balancer decides which request goes to which server. It sits in front, receives every request, and forwards each one to a healthy backend.
Strategies vary: round-robin takes turns, least-connections picks the idlest server, and health checks pull dead servers out of rotation automatically. The result is that no single machine gets overwhelmed, and one server failing doesn't take your site down.