An integer is a variable that specifically holds a numerical value. A string is a variable that can hold a range of characters including numbers. String variables are usually enclosed in inverted commas.
GunBroker requires that your categories be integers, which means that the category can only contain numbers. When you navigate to Queued Listings-->Product Details (binocular icon), you will see a menu of categories. Once you select the correct category, you will see a number show up in the field box next to the category.
Once you have selected the correct category, click the blue "Save" button, and then try re-listing your item.