Some amusement parks charge a general admission fee, to the park as a whole. Once you are inside, there might be some things that you can do without paying an additional fee, but some activities do require an additional payment for participation. You can limit your enjoyment of the amusement park to the no-fee or "free" activities, or you can pay more for the really exciting stuff.
The park whose advertising you have seen follows a different policy. It charges one admission fee to get in, and once you are in, no ride or other activity within the amusement park requires payment of anything more. So all events are free [of additional charges] with [payment of the general] admission [fee].
You can presume that the general admission fee is higher than it would be for an amusement park with exactly the same rides and activities but extra charges for some individual activities.
An amusement park might also have no general admission fee but charge individually for every separate ride or other activity you do there.