What on Earth is the subjunctive?

It can be hard for native English speakers to fully grasp the subjunctive mood, because it’s so archaic in English. Firstly, it’s a mood and not a tense. It emphasises that somewhere in your sentence there is an element of doubt, and it is triggered by certain phrases. Bien que/quoique (although) is a key example. Bien que je sois content....
There’s no definitive list of expressions that trigger the subjunctive, and how it affects the verb (eg. Je suis becomes je sois) is something you just have to learn by heart.