This function available at all Wikipedias where a list of mentors has been created and activated.
Since May 2019, the Growth team is working on the Newcomer homepage project. This feature is only available on a short list of wikis.
Part of this project is to assign each newbie an experienced mentor. This mentor is randomly selected from the list of experienced users who volunteered to be mentors.
Originally, it wasn't possible to change the mentor, which could've caused some troubles for wiki instructors, who might want to be a mentor for all their participants, and also for other groups of people. Since January 2020, it is possible for any listed mentor to change the assigned mentor for any newbie.
Since November 2020, it is possible to register as a mentor who can only claim mentees, but not being assigned to random mentors. The procedure to claim the mentee is the same, as for regular mentors. To enable this feature, a wiki needs to create a separate list, and ask for a configuration change to be made. For more information, see information about separate list.
All usages of this interface are logged at Special:Log. If you want to filter just Growth-related changes, you can use Special:Log/growthexperiments.