This is an extremely common setup.
The top lock is a deadbolt. A deadbolt, within the limits of design (some types of locks are easier to pick than others) and installation (a lock is in a weak door or a weak frame then it will only be as secure as the weakest part) is generally very secure. In general, getting past a locked deadbolt requires some violent action - breaking the glass to reach in and turn the latch (which is actually a very real problem with glass doors or with doors that have a glass panel next to the door, but for fire safety you don't want to have a double-cylinder (key needed inside or out)) or cutting into the door or frame.
The bottom lock is, well, not much of a lock. It doesn't provide much security. It is enough to keep pets and (friendly) kids out. But it does very little to stop a determined adult. It is often trivially easy to pop open the lock with a screwdriver or sometimes even just a credit card. A telephone guy I worked with once referred to a flat screwdriver as the "universal key" because it works quite well to get into any telephone closet that doesn't have a deadbolt. In fact, I actually recommend disabling the lock mechanism on this type of lock, particularly if it is designed such that you can accidentally lock yourself out. With a typical (there may be exceptions) deadbolt you can't lock yourself out. But with a lock like this you can lock yourself out while at the same time doing little to prevent the bad guys from getting in.
In other words - use the top lock for security, and use the bottom lock just for the handle to open/close the door.