They serve the same function as an electromechanical relay, but solid-state electronics contain no moving parts and have a longer operational lifetime.
Packaged SSRs use power semiconductor devices such as thyristors and transistors, to switch currents up to around a hundred amperes.
SSRs have fast switching speeds compared with electromechanical relays, and have no physical contacts to wear out.
The circuit will never be interrupted in the middle of a sine wave peak, preventing the large transient voltages that would otherwise occur due to the sudden collapse of the magnetic field around the inductance.
Applications which require Time Critical On/Off switching, should use Transistor or MOSFET design types as they are not subject to the inherent Zero Cross variations that SCR or TRIAC devices will exhibit.
Proportional SSRs can delay the onset of voltage after the zero crossing in order to lower the current output (phase angle control).