That means you have an app waiting for you to update. The only way to get rid of that red badge on the App Store icon is to update the app that's ready for the update.
If you open the App Store and tap the Updates button at the bottom of the page, the list of all apps awaiting updates will appear. If you want to update all of them, tap the Update All button at the top of the page.
You can turn off the badge showing the number (in Notifactions) but unless you have automatic updates set on, you will not be signaled that you have something to update.