Electromagnets allow us to create controllable magnetic fields, i.e.: they act as magnets that we can turn on and off as we please but controlling an input voltage.
Compare them to permanent magnet: on a magnet, you always have a fixed generated magnetic field. But with an electromagnet you can control the field, and even turn it off entirely.
This type of "useful looking thing that can be controlled by a voltage" tends to be of huge importance in electrical engineering, the transistor being another example.
Solenoid means "tubular" in Greek.
Solenoids are simpler to build as they don't require insulated wire as in modern electrical cable because as the electromagnetic coils don't touch one another.
As such it is perhaps the reason why some early electromagnetism experiments were carried out with solenoids, which André-Marie Ampère named in 1823.
But the downside of this is that the magnetic field they can generate is less strong.
Magnetic field lines around a solenoid cross-section
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