Electromagnets are used in all kinds of electric devices, including the familiar hard disk drives, speakers, motors and generators, as well as lifting heavy material like metal scrap. They're even used in MRI machines (Magnetic resonance imaging) in Health Care industries. The magnetic field is produced by an electric current and disappears when the current is turned off.
The retentivity of a material is its capacity to remain magnetized even after the external magnetizing field has ceased to exist. A material with high retentivity such as iron will retain the magnetic properties and it can even become a permanent magnet (it can get magnetized), whereas a material with low or no retentivity can not retain the magnetic properties. Therefore the material used in an electromagnet should have low retentivity, so that it doesn't get magnetized, or gets demagnetised easily.
Coercivity is the magnetic field intensity needed to reduce the magnetization of a ferromagnetic material from complete saturation to zero, or to fully de-magnetize the material, usually measured in teslas or amp/meter.
When we make a solenoid core, we would mainly be interested in a material which exhibits low eddy current losses (eddy currents are induced during a change in field, and they result in heating / losses in the core - this is not desirable except in the case of induction heating), and with high permeability - the latter enhances the magnetic field. Also,we want high saturation - i.e., to be able to make a strong magnetic field, we want the material to remain linear (the more the atoms align in the field, the stronger the over all induced field becomes). These reasons make soft iron a good material for DC electromagnets; we can get a very high field from them.
However, the conductivity of soft iron gives rise to eddy current heating when it is used in an AC applications (also known as Hysteresis loss) - for example, in AC transformers. For this reason, it is usually laminated (cut into thin slabs or lamina which are electrically insulated from each other). This prevents eddy currents, and limits the heating. The most common material used is Cold Rolled Grain Oriented iron.)
A ferromagnet with a low coercive field like this is considered soft and so ideal for electromagnets.