a magnetic domain

Here is a puzzle: iron is ferromagnetic, so all its atomic moments want to align, yet a fresh iron nail out of the box is not a magnet and will not stick to your keys. The resolution is that the alignment happens only in small patches. A magnetic domain is one such patch, a region, maybe micrometers across, where all the moments do point the same way, but different domains point in different directions, so overall they cancel.

The material breaks itself into domains because a single giant uniformly magnetized block would spray magnetic field into the space around it, which costs energy. Splitting into domains that point different ways lets the field close on itself inside the material and lowers the total energy. Between two domains is a thin transition region called a domain wall, where the moments swivel gradually from one direction to the next. When you apply an external field you magnetize the material not by rotating every atom at once, but by moving these walls so that domains already pointing the favorable way grow at the expense of the others; push hard and the last unfavorable domains finally rotate to give saturation.

Domains explain almost everything about practical magnets. You can sometimes hear the walls jump in sudden clicks (the Barkhausen effect) as they tear past defects. Whether a material is easy or hard to magnetize comes down to how freely its domain walls move: obstacles like grain boundaries, precipitates, and impurities pin the walls, and pinning is exactly what separates soft magnets from hard ones. A common misconception is that magnetizing iron creates new magnetism from nothing; really it just reorganizes domains that were already there but cancelling.