Usually you will be asked how much of your costume you made, what materials you used, how you created particularly unique or difficult things... sometimes they'll ask how long it took to make or if you had any help. They might ask more mundane things like what the hardest part to make was.
Overall it's going to be about the craftsmanship of your costume and the process, because that's what they are there to judge. So to prepare, make sure you know the materials and tools you used and be able to explain how you made things. Also make sure you are prepared to tell them any cool details they might not have picked up on, like if you hand-embroidered something, or made your own shoes instead of building off of existing shoes. It helps to keep a portfolio of the costume with swatches, photos, receipts, etc., but it's not usually required unless you are entering at a Masters level or competing for Best in Show.