The variable timing solenoid is an actuator used to vary the camshaft rotation that controls when the valves that let intake air and exhaust gasses out of the engine. By having variable cam timing and being able to fine-tune when the valves in the cylinder head open and close the engine computer can adjust their opening for better power and emissions under specific driving conditions.
The variable cam timing system works off engine oil pressure. There is a solenoid (valve) that controls how much pressure is applied to an actuator built into the camshaft's drive sprocket. When the timing chain driven off the spinning crankshaft turns the camshaft drive sprocket, the variable actuator can advance or retard (i.e. move ahead clockwise or retard counter-clcockwise) the camshaft a certain number of degrees rotation in either direction. Engines with fixed camshaft timing (i.e. the camshaft rotation never varies and is tied directly to the crankshaft movement) don't have this actuator and instead just use a regular sprocket.
Because the variable cam timing system used oil pressure to control the actuator to adjust cam timing, if the control solenoid (that controls amount of oil pressure) or the actual solenoid leaks you might have to replace something as simple as an o-ring seal or the entire component to correct a leak. Depending on the mileage and how old the car is it might be covered under a powertrain warranty. Since this sounds like an independent oil change type place and some of these repairs could cost a fair amount of money, it might be wise to get a second opinion. If the car is under warranty a dealer might be best.
Lets say you do have a minor leak. If its just a small sign of oil weeping out and it isn't building up it might not be worth the effort to repair unless it gets worse. Again that's something a second opinion might help guide you on how important it is.
