***** NOT A TEACHER *****
Hello, Anil Giria:
Don't feel bad. I have found that many learners are completely confused about "to be." In my opinion, they do not spend enough time learning "to be." They rush on to more interesting verbs before they truly understand "to be." Big mistake, in my opinion.
1. Yes, you are right: sometimes "to be" is simply an auxiliary (helping) verb: "I am writing this post to you." If I said, "I writing this post to you," you would understand. But English requires an auxiliary verb. It helps with the tense: am / was/ will be writing.
2. In some languages, people say "He a good boy." But in English, sentences require a verb. So native speakers use "to be" as a connecting or linking verb. We have to say "He is a good boy." The linking verb "is" joins "he" and "a good boy." Furthermore, we can say: "He is / was / will be a good boy."
3. Finally, occasionally "to be" is NOT an auxiliary verb and it is NOT a linking verb. It is a full verb. That is, it is a verb like "eat," "play," "read," etc. It means something like "to exist."
a. Mona is at home.
b. You have probably read Shakespeare. So you probably know that famous line: "To be or not to be: that is the question." (In other words: To exist / live or not to exist / live: that is the question.)
James