Instagram's Photo Map feature lets you plot your pictures on a map of the world using the geolocation data embedded in the photos, but it's an optional extra rather than a compulsory requirement. The feature is disabled by default. If you use the Maps feature, you can remove images from the map one by one.
Adding to the Photo Map
Whenever you post a new photo to Instagram, the final screen in the process offers an "Add to Your Photo Map" option. This is switched off by default, so unless you specifically turn it on, the content won't appear on your map. If you do enable the feature, you have the option to name the location where the photo was taken.
Viewing Your Photo Map
You can access the Photo Map by tapping the map pin icon on the Profile screen. The first time you open up the map, you'll be prompted to review all the images you've previously taken that have geolocation information stored with them; deselect all the photos that you don't want to appear on the map. From the Photo Map screen, you can zoom in and out of various locations, view your photos in a grid and explore sets of images taken at the same place. Double-tap on a stack of photos to see them in a grid layout.
You can remove images from the map on the Photo Map page itself. Tap the menu button in the top right corner of the Photo Map screen and choose "Edit." Deselect any pictures that you don't want to appear on the map. Any images you remove remain in your Instagram feed, but the geolocation information associated with them is deleted permanently. If you want to restore a picture to the map you must upload the image again.
Photo Map Privacy
If you have a public account, anyone on Instagram can view your Photo Map by tapping the map pin icon on your profile. If you have a private account, any of your approved followers can view the map. If you don't have any photos on your map, the icon is disabled and doesn't lead anywhere. To remove the photo map completely, you must deselect all the images that are currently on it.