On Instagram, if you post beautiful photos, you tend to get more likes. Other users can repost your photos if they have the app, but most of the times, Instagram likes comes from other users who browse the “Search” section of Instagram.
If you hash tag your photos correctly, more people will get to see them. And usually, for an Instagram user, if a photo they like is intriguing enough, they will visit the owner’s profile. From there (if your account is not set to private, that is), they will view other photos. If you happen to have a gallery of awesome photos, other users will usually follow your account. While Instagram likes is not the main reason a user follows another user, it’s definitely one of the strongest factors in drawing in and attracting more followers.
What you can do is try to take great photos for your Instagram account. With advanced smartphones and beautiful filters, this isn’t a very hard thing to do anymore even though you would still need to have the eye for a great photo.