What is the word that describes when someone uses the definition of a word instead of the word itself?
It can be called periphrasis or euphemism, but there are some differences between the two.
If you only use a definition instead of the word it is a periphrasis.
An example of peryphrasis could be:
A quadrilateral with 4 equal angles and sides instead of the word square
Both definition and word are neutral so it is not an euphemism but just a peryphrasis
If you want to use another word or definition in place of one you think is too harsh when referring to something unpleasant then such device is called euphemism.
An example of euphemism could be if you said
passed out instead of died
The phrase to pass out is a milder way to say about someone's death so it is an euphemism.