You will want to track various activities on your Instagram account, including new followers and accounts that have unfollowed your page. Unlike Facebook, Instagram does not have its own analytics tool.
One tool you can use, mentioned above, is Iconsquare. It was formerly called Statigram. Iconsquare can provide analytics around most popular posts, average number of comments, and so on.
InstaFollow is another tool you can use. This tool specifically tracks information about followers, such as new follows and unfollows.