Amusement is a state or feeling of mirth. For example, If someone looks on with amusement at something, they find it funny. An amusement can also be something someone does for fun or for diversion, such as playing a game.
Ex: My mother always watches her grandchildren with amusement as they try to follow her recipe for chocolate brownies. Seeing the girls covered in flour and the boys doing more eating than baking brings a huge smile to her face.
Ex: At the carnival, the group of boys found lots to keep them entertained. They played at stalls featuring balloon darts, ring throws, and several other amusements.
An amusement park is a large space out of doors where people go to be entertained by rides such as roller coasters, games, shows, and food and drink.
Ex: When it rained all morning at the amusement park, many of the guests waited in the queue to see if they could be granted a voucher to come back and enjoy the rides another day.
Ex: True roller coaster enthusiasts will travel quite a distance to try out the newest thrill ride, even if it means going to an amusement park in another state.
Excitement is a state of being enthusiastic or eager about something. In many cases, but not all, excitement has to do with the anticipation of something.
Ex: The boy's excitement about attending his first auto race could not be quelled. His father finally gave up trying to quiet him and simply waited for the race to begin.
Ex: The excitement in the room was noticeable as the manager entered. Everyone knew that the person recognised as employee of the year would receive a significant bonus.
The expression on the edge of one's seat is to be excited about something about to happen, for example, the final results of a game or the end of a movie. It calls to mind the idea of literally moving forward in a seat as you become engrossed in an event or scene.
Ex: My sister, who lives across the country, is having her first baby today. I am on the edge of my seat to find out if it is a boy or a girl!
Ex: I will probably be finishing the mystery novel I have been reading for 2 weeks this evening. I can't wait to get home, get a cup of tea and find out how it ends. I am on the edge of my seat!