The RPG elements happen on your base ship, called the Raven, where you can talk to advisers, generals, your princess, etc and get/complete tasks, and make various decisions (more than in Larian's previous RPGs).
When you leave the Raven, you get to the TBS part, a board game like tactical world map, where you can move troops around, use bonuses you have collected, decide which generals to use, and which battle to take part in yourself. Larian made an actual board game to develop / test this part, and IIRC someone said it might end up as one of the multi-player modes.
The last phase is real time combat, where you can fly around as a dragon and/or direct you allies on what to do, or you can zoom out to a battlefield overview map and play it in RTS style.