What is it?
A Challenge checker is a piece of program code that will check if a user have completed the requirements of a challenge cache, per the guidelines of Geocaching.com a challenge cache published after April 21, 2015, must include a link to a web-based challenge checker.  So far Project-GC is the only allowed challenge checker.
How does it work?
A challenge checker consists of two parts: a challenge checker script and a tag. The checker script is a piece of program code written in the programming language Lua. The same checker script can be used for multiple challenge caches (For instance, most calendar challenges are handled by the same checker script). The tag is what makes this possible. The tag links a checker script, a challenge cache, and (optionally) a set of parameters for the checker script. This means that the same checker script can be used both for a challenge that requires the user to have found 100 mystery caches and a challenge that requires the user to have found 1000 traditional caches, since the cache type and quantity of finds required is specified in the tag.
Project-GC also calculates how difficult a challenge is, more information at: Challenge difficulty
Challenge checkers are created by volunteers and can be requested in the Checker request forums, make sure you read the READ FIRST-post before posting your request.
Visit Project-GC's FAQ to find answers to many of the most common questions.
Related paid membership feature
With a paid membership there is no limit on how many challenge checkers you can run. Non paying users are only allowed to run 10 challenge checkers per 24 hours. The limit is a rolling rate limit.
The checker script system can be used to create different tools to check for statistics that are not otherwise available at the site. See Tools in the checker system for more information.
- Guidelines for Challenge caches at Geocaching.com's Help Center.