A "solenoid" is basically an electrico magnetic safety valve that for example allows fuel or gas to flow.
In example.
an electrical current is passed to the solenoid which energises it, then it opens and allows the fuel to the injectors.
In a boiler for example
The fan runs, an air pressure switch detects air flow, a spark is generated, the solenoid opens and allow gas to pass to ignition.
Your solenoid is playing up, you need to get the electricals checked along with any engine management system components...
Phil, January 2012