An Instagram loop giveaway consists of multiple Instagram accounts collaborating to host a giveaway with the goal of increasing followers and engagement for all participating accounts. Those Instagram influencers set out a prize or present (giveaway) which they promote on their accounts with specific instructions how to enter the lottery for winning the giveaway. This typically consists of following all the accounts involved in the loop and/or tagging their friends to attract even more users.
By having users follow all the accounts in the loop and tag their friends, the participating accounts gain more followers and increased engagement during the giveaway period.
At the end the organizing influencers select a random winner who then receives the giveaway.
Originally, such a loop giveaway was organized by some influencer friends who joined to benefit from each others follower community [0]. However, nowadays it is oftentimes the case that one of the big influencers organizes and promotes the giveaway and hence reaches a lot of users. Smaller influencers typically pay money to that giant influencer to be on the who-to-follow list. Often, opportunities to buy into giveaways from big influencers are advertised on private Telegram groups, such as 450€ for 5,000-10,000 new followers. [1]
This strategy is likewise used by personal and brand instagram accounts.
However, loop giveaways are also somewhat controversial, as some users see them as a way to gain temporary followers who might not have genuine interest in the content, leading to potential drops in engagement after the giveaway ends.
[0] https://jumpermedia.co/all-about-instagram-loop-giveaways/
[1] https://www.vice.com/de/article/88najz/loop-giveaways-das-riesengeschaft-mit-echten-followern-auf-instagram (in german)