Twitter engagement pods are groups of people making a promise to each other: To mutually like (and eventually comment or retweet) each other's content. Historically done over discussion groups, Twitter engagement pods are now automated: Every time a member of a group publishes a Tweet, every members of the engagement pod will automatically like it.
By automatically liking Tweets via an engagement pod, you do something very powerful: Tweets have an average lifetime of 5 minutes. Meaning that after 5 minutes, most Tweets will just never be displayed ever again. By receiving likes right after publication, your tweet's lifetime is increase, it is displayed in your followers feeds, then in their audiences giving it way higher chance of being seen.
Human are biased in many ways. One of them is trusting things that have already been approved by others. By joining an engagement pod, you'll systematically have numerous likes on your Tweets. People finding out about your content will take it much more seriously than Tweets unapproved yet by others.