In Super Mario 64, each of the main fifteen courses have six Acts. These Acts, also referred to as Missions, represent different iterations of each level, with each Act being named after its corresponding Star.
The purpose of having separate Acts for each Star is that it allows the game designers to swap out certain elements that either enhance the gameplay for that Star, or provide extra challenges. For example, the six Acts for the third course, Jolly Roger Bay, are used to change the positioning and behaviours of the sunken ship as well as Unagi, the giant eel.
The names of each Act are intended to be hints pertaining to the Star's location, or the method required to spawn/obtain it. In many SM64 ROM hacks, creators have begun including certain suffixes or acronyms to indicate the requirement of a Cap Switch's activation. For example, the final Star for course one in SM64: Decades Later is called Mario Wings To The Sky -WC-. The "-WC-" added onto the end indicates that the Wing Cap is required for to obtain this Star.
Acts are a feature exclusive to main courses. Other areas such as secret courses, Bowser levels, and overworld areas, do not have an Act Select screen, nor any Act displayed on the pause menu.
On this wiki, the Act names are italicised and have each word capitalised. This is because in-game dialogue refers to the Act names also being the names of the Stars, and that's how the names of people are capitalised; the italics is more to make it stand out as a significant string of text.