subjunctive mood: This is a verb form used when talking about hypothetical, wishful, unreal, uncertain, imaginary, improbable, impossible, or untrue situations. Subjunctive mood has all three tenses but only two are still used in modern English: the present and the past. And of those two, really only the past subjunctive is worth discussing in the context of ESL:
Simple Past Subjunctive Past
I was I were
You were You were
He was He were
She was She were
It was It were
For an ESL teacher, the most important subjunctive to know is the past tense form as it is used when speaking hypothetically or when using the second conditional.
If I were you, I would stop bugging your teacher.
Impossible: I can't be you
If I won the lottery tomorrow, I would split it with you.
Improbable: It is unlikely that I will win.
I wish I were home in bed.
I wish I talked to her earlier.
Wishful and Untrue: I am not home in bed. I didn't talk to her.
There are numerous other uses for the subjunctive mood but most ESL teachers have bigger fish to fry. Another subjunctive mood relic is the lack of a third person singular when making suggestions and demands:
I insist that he never be admitted here again.
I suggest she go to the Italian place.
We use she go and he be instead of she goes and he is.