To inflect is to speak in a way that reflects — and changes with — your mood. After hearing tragic news, you'll inflect what you say with the sadness you feel.
The changing pitch of your voice inflects your words with meaning, and another way to inflect is to change the form of a word for grammatical reasons, including tense, number, or gender. When you inflect verbs, it's also called conjugation. For example, when you change the verb "to be" from "I am" to "we are," you inflect it. The Latin root of inflect is inflectere, "to bend," and also "to change."