A moving charge gives rise to an associated magnetic field.
In the case of atoms, negatively charged particles called electrons revolve around a centre called nucleus.
These electrons are responsible for the creation of magnetic field.
We call the magnetic effect due to a single electron, it's magnetic moment.
The magnetic moments can occur in any direction.
A Domain is simply a collection of magnetic moments.
All matter have this domain.
If in a domain, the magnetic moments are aligned in the same direction, and all the domains are also aligned in the same direction, then the particle is attracted by a magnetic field.
If the magnetic moments in a domain are randomly aligned such that it has no net magnetic moment (one cancels the other) , then that particle is non-magnetic in nature.