A label is a tag that you can put on to any affiliate/publisher/partner, offer, and advertiser. This is meant to be a completely customizable system of tagging that is searchable. You can also run reports on labels in the flex and dynamic nested reports. You can add a label during the offer setup or when you edit an offer. It is located under the "General" tab. Type any label text you want then hit enter to create it.
It should look like this when it is created. Remember to hit "Save" at the bottom of the screen.
Categories are a system in which to identify what traffic type group an offer falls into. Examples of categories would be "Gaming", "Lead Gen", "Clothing", and "Retail". You can customize the categories by going to Network >> Categories
You can attach a category to an offer during the offer setup or when you edit an offer. It would be located under the "General" tab.