An inaugural is a ceremony inducting someone into a new position, especially the President. We also call the President's first speech an inaugural address.
This word has to do with ceremonies and firsts: an inaugural or inaugural address is the first speech made by a President at a ceremony also called the inauguration. This word is highly associated with Presidents, but it can apply to any kind of official first. An inaugural trip to China is a first trip to China. If you want to make a first sound fancy or important, try inaugural.