Après (without que) is usually followed by a noun or an infinitive, but not a subject. With the addition of que, you can have a different subject in the après-clause than the main clause.
Après le dîner je vais aller me coucher. -- After dinner, I am going going to bed. (Same subject between the two clauses -- je)
Après avoir fini le dîner, je vais aller me coucher. -- After having finished dinner, I'll go to bed. (Again, je is the common subject of the two clauses.)
Tu vas aller te coucher après que nous avons fini le dîner. -- You'll go to bed after we have finished dinner. (Here the subject between the main clause -- tu -- is different from the one in the subordinate clause -- nous).