What are double-sided cards or whatever?
Yeah, as stated they're cards that have two sides. They 'transform' or flip over when a certain condition is met. The state of the card is preserved in every other way, so enchantments, counters, equipments, and other things on that creature are still there, the creature simply has different properties now.
There's a DFC planeswalker as well, Garruk Relentless/Garruk the Veiled Curse, but I can't find a good image at the moment.
The intention is that you're supposed to play these with opaque-back sleeves, and only have the 'day' side, or the side with the mana cost, revealed by the clear side, and then physically pull them out of the sleeve and flip them over when they transform. If you don't have sleeves, you're expected to use a 'checklist' card in your deck instead, it looks like this:
and the card you're playing is meant to be obvious through you making a mark or check on the intended creature-name beforehand, with a sharpie or something, and then when you cast it, you physically substitute the checklist card with the actual DFC that you had hidden in your sideboard or deckbox or something.
Wizards is trying to make sure that players get enough of these by placing them in packs substituting the land spot in 3/4 of all boosters.
It's a hell of a lot to take in, and I seriously don't like it.