It's specifically the first person singular present tense form (I am).
"To be" is a special verb called a "copula" or "linking verb" because it connects the subject of a sentence to its complement (usually a noun or adjective).
Here's how to identify it:
* It expresses a state of being: "I *am* happy."
* It links the subject to an adjective or noun: "She *is* a doctor."
* It is used in the present tense: "We *are* here."
So, "am" is a verb that's part of a crucial group of verbs that help us describe existence and states of being.