FIRST Choice by AndyMark
AndyMark has been hosting FIRST Choice since 2012.
It has had many variations in the past, and has grown into a Priority List system, where teams in the FIRST Robotics Competition program select items of their desire with available quantities and in the priority preference of their choosing. Once a deadline is hit, an automated process runs through all the entries to approve what items the teams get, based on some factors.
Each year can be slightly different, so you'll want to keep up to date with the information sent out by FIRST, and not rely on how it worked in the past.
The video here shows how FIRST Choice worked in the 2020 FRC Season.
The most up to date and accurate information can be found in the FIRST Choice section of the Kit of Parts page.
2021 Timeline for all events can be found on the process flow chart