A magic ring or a magic circle is a technique to begin crocheting by passing the first through a loop next to it and then pulling the knot tight. A lot of the older patterns used tend to end up with a hole in the center of the round that you may have created. The stitches could be loosened due to the hole in the middle. This makes your work look really untidy and unprofessional.
Using the magic circle crochet method creates a neat closed circle in the center of the first round without any holes left. It is popular not only when making amigurumi and rugs, but people often use it when making shawls and hats that are worked top down as it allows you to use more stitches in the first round as compared to the other methods where you can’t form more than one stitch.
Read more about Crochet at https://5amily.com/crocheting/blog/magic-circle-crochet-explained