"Is" is a verb, but it's specifically a "be" verb. Be verbs** are a little different from other verbs. They don't show actions but instead describe a state of being or existence.
Here are some examples of "is" as a verb:
* The sky is blue. (describes the state of the sky)
* She is a doctor. (describes her profession)
* This is my house. (indicates possession)
Let me know if you'd like to know more about "be" verbs!