Neodymium magnets are considered strong because they resist demagnetization and have a high saturation magnetization. The saturation magnetization is related to the magnetic energy a material can store, so it’s an indicator of the physical pull strength the magnet can achieve.
A neodymium magnet is actually an alloy of neodymium, iron, and boron that forms a crystalline structure with formula Nd2Fe14B. Ferromagnetic materials like neodymium magnets are composed of microscopic regions called magnetic domains that align in the same direction when exposed to an external magnetic field. When practically all the domains are lined up, the material is at it’s saturation magnetization. At this saturation point, a neodymium magnet has a stronger magnetic field than other magnets.
The symmetry of the atoms in the tetragonal Nd2Fe14B crystalline structure causes what is called high uniaxial magnetocrystalline anisotropy. This means that the crystals have one axis that doesn’t require as much energy to magnetize, so if the crystals are subjected to a powerful magnetic field, they will all point in the same direction along their “easy” axis of magnetization. When a crystal has one easy axis of magnetization, the coercivity, or resistance to demagnetization, of the material increases because more energy is required to change the direction of magnetization.