What does it mean that "am" is the first person singular present indicative of "be"? What is the definition of "am"?
"am" is the form of the verb "to be" used with the first person singular subject.
Let's try to break this down:
The basic form of a verb is usually expressed as an "infinitive" e.g. "to do", "to make", "to run", and so on.
When used in a sentence a verb is modified to indicate when the "action" took place and the subject that "performed the action".
"when" an action took place has three simple forms (with multiple sub-forms):
"subject" has two components:
In English, the subject may be:
to be is an "irregular verb"
This means that it does not follow the most common patterns for forming the verb agreement with "when" and "subject".
As can be seen from the above, if we wish to indicate (use the indicative) of the verb to be to express the present state for the first person we should use the version: am