The transmission interlock is a safety device found on some cars and other vehicles, which prevents the engine from being started when the transmission is in gear. This prevents you from starting your car in gear and having it move unexpectedly, or damaging your starter motor.
The transmission interlock usually works by interrupting the connection between the ignition switch and the starter solenoid with a microswitch mounted on the transmission's selector lever.
Sometimes the interlock switch will become defective or misaligned, preventing your car from starting. If the starter won't kick in, and wiggling the gearshift lever brings it to life, chances are the switch is loose in its bracket or failing.
On a vehicle with a stick shift, the interlock is usually a switch that disables the starter unless the clutch pedal is fully pressed. This sort of switch becomes misaligned far more often, but is usually easy to adjust.