Prologue is the start of the game but remastered, to put it simple, it's the same game but better (I hope xD )
It's mostly a visual improvement, but it will also have extra stuff that the original didn't have like animations, gallery more endings, more side quests and certain game mechanics will be improved. There's more stuff, nothing like playing it to see though.
To play Act II you need to reach the correct ending on Act I (You need to speak with Sloth) He will tell you to create a Special savegame, Act II will then recognize that save game when you press start. (The name of the save will be the one you gave it on Act I)
PS: If you are using android you need to allow the App to save files on your device.
Cheers!