This refers to the different levels of comparison made by adjectives and adverbs. There are three degrees, positive, comparative, and superlative. For example:
The good dog. (positive; no comparison implied)
The better dog. (comparative; comparison between two implied)
The best dog. (superlative; comparison between three or more implied)
Adverbs can also have degree:
She ran fast.
She ran faster.
She ran fastest.
cf. principle 32.