The Pier is the first place new arrivals to the Island will see. The higher the Pier's level, the more tourists can arrive at once. When tourists come to you, a suitcase icon appears above the pier. Click on it, and all arriving tourists will instantly be available for use in organizing events.

Tourists can come to the Island instantly if you speed up the process. In the Pier menu, click on the speed up button.
The amount of coming tourists is also increased by decorations on your island. The more decorations you have, the more tourists come. In the pier info-window you can see the total number of arriving tourists. In the brackets you will see a number of tourists, attracted by decorations only. For example, if you see +1000 (+800), it means that 1000 tourists come in total, and 800 of them are attracted by the decorations you have (thus, 200 of them are determined by the pier level).
AS you play, number of arriving tourists will grow. One day you will have a lack of free rooms for them. In this case you won't be able to accept all tourists. You should either send them away, or build more hotels.