can of worms is right.
Nuc is short for nucleus. I would consider it to be the heart of the hive, kind of like the heart of a watermelon, it is the best part.
I sell some five frame nucs in the late spring, I make mine from splitting overwintered hives in two. Dividing up the brood and stores. Of course there will only be one queen from a split and there are several ways to address this.
1. Let them make their own queen, you must be sure there is eggs in the queenless hive. A walk away split is where you divvy everything up and make sure you have eggs in both splits hoping that the queenless hive makes a queen.
2. Introduce another queen from some you or somebody else raised.
3. Install queen cells.
The nucs I sell are five frame deep nucs and need to be transferred into a 10 frame box immediately to prevent swarming. Two frames of brood in all stages, a laying queen, two frames of honey and pollen, and a frame that is in progress.
Some sell nucs in 2, 3, 4, 5 frame configurations an deeps or mediums.
Mating nucs are a little different they, are used for virgin queens to live in, take their mating flights and return to start laying. When they are proven layers they are plucked out and sold or installed into anther hive. These can range from three frame minis to five frame deeps.