I do drive a car with manual transmission, which has 5 forward gears and one reverse gear. I need to put my car in gear to drive it. The higher number of the gear I shift the car into, the faster it can run. I think this can explain what "gear up" means as verb.
In the song of "Friends", there is a famous line "life is always stuck in the second gear ..."
second gear is what you do in the parking lot. If life is always stuck in the second gear, it sucks...:)