The 700 means 700C. This is a designation for the diameter of a standard modern road wheel (it is based on a French system for classifying bike wheels, don't worry about that). The 38 is the diameter of the tire in millimeters. As far as how narrow you can go, that depends on the width of your rim. You can measure that yourself.

Some typical tire widths are 35, 32, 28, 25, 23. Your rims are probably a bit wide, so I expect you can go to 28mm for sure, maybe 25. For a recreational rider on a hybrid, I think 28 to 32 mm tires are a pretty good compromise in terms of balancing speed and comfort, depending on the weight of rider and bike.

I see FB beat me to the punch. I think Bike Forums might be wired directly into his head. I gotta quit posting here.