A web page is said to be built on-the-fly when the page is "constructed" as the user loads it in their browser. Usually this involves dynamic content, where the page is built up of content pulled from a database, depending on the user's actions.
For example, the pages in this dictionary are built on the fly. When you click a letter, the page loads all the matching terms from the database onto the page. When you click on a different letter, the same page loads, but with different content being pulled from the database.
This is usually achieved by using a server-side scripting language, such as PHP in the case of this dictionary.