What is the relationship between something magnetic and unpaired electrons?
There are five forms of magnetic behavior. Ferromagnetism is when a material is attracted to a magnetic field and can spontaneously hold a magnetic field alone (the typical form of magnetism).  Paramagnetism is when a material is attracted to a magnetic field but cannot spontaneously hold a magnetic field alone (the attraction may be too weak to observe practically).  Diamagnetism is a material that expels magnetic fields (essentially non-magnetic). there is also ferrimagnetic and anti-ferromagnetic but though these are interesting they not incredibly relevant to the answer.

Electrons form the magnetic fields of materials.  If a metal's atom have unpaired electrons the metal can attract a magnetic field.  If all of the electrons are paired in opposite spin orbitals then the spins cancel each other out and no response to a magnetic field is observed. 

Cobalt has unpaired electrons making it at minimum demonstrate paramagnetic behavior. It is however able to hold a magnetic field making it ferromagnetic.  Most metals have unpaired electron and are paramagnetic (for example: aluminum, zirconium, titanium, magnesium and potassium)  Ferromagnetic metals become paramagnetic at elevated temperatures and inversely many paramagnetic metals become ferromagnetic at low temperatures.