The subjunctive often expresses doubt - it is more like a mood than a tense. If something is uncertain we use the subjunctive.
A useful way to remember some of the cases in which we often see the subjunctive is: WEIRD. (it is a 'weird' grammatical feature that we don't have - that's for sure)
W - wish E - emotion I - impersonal expression R - request D - doubt
So with expressions such as: "J'espère que...", "Je suis heureux/euse que...", "Il faut que...", "Je veux que..." and "Je doute que..." we would see the subjuctive.
What is important to note is that in some cases where the positive uses the positive (i.e. je pense que..) uses the indicative the negative (i.e. je ne pense pas que...) uses the subjunctive because it is conveying doubt.
It's this difficulty that makes the subjunctive so impressive when you use it in your essays/written responses.
Any other questions? Is anything unclear? Does anything else need explaining?