The transmission control solenoid communicates to a car when it is time to shift gears, if the car has an automatic transmission. If the shifting in the car's engine is balky or has other problems, the issue is likely an error with the control solenoid. Because a fairly sophisticated measurement of hydraulic pressure is necessary to operate the transmission, a solenoid that loses sensitivity to this factor is headed for repair or replacement.
Even with modern electronics governing transmissions, the operating principles that they follow are still mainly hydraulic, requiring a more precise control on the pressure. Older designs for automatic transmissions just use one line with a pressure control solenoid, adjusting pressure throughout the whole transmission. Newer designs require multiple pressure control solenoids, sometimes permitting the solenoids to apply exact pressure controls. It is the shift pressure that affects shift quality; if there is too much pressure, the shifting gets rough, but if there is not enough pressure, the clutches overheat.
If the shifting shows signs of problems, take the car to a certified mechanic to have the troubleshooting codes of the engine checked. Often that is the only clear sign of a problem until the power steering simply gives out, so be proactive. Regular maintenance and inspection can aid in the early detection of mechanical issues and save money on potential repairs.