If you do something in a fearful, cautious way, you act timidly. The best teachers take care to call on the students in the back timidly raising their hands, not just the eager chatterboxes in the front row.
While it's not a good idea to speed through the streets in your car, driving timidly can be a problem too, since your nervousness might cause you to slam on the brakes unnecessarily or drive too slowly. It's understandable to speak timidly when you're asking a famous movie star for an autograph or for an extremely shy person to behave timidly at a social event full of strangers. The Latin root of this word, timere, means "to fear."