Summary: A bicycle helmet offers a lot of protection, but you can exceed its capacity and be injured.
Under US standards bike helmets are tested in 2 meter drops that achieve about 14 miles per hour (22.5 kph) on the flat anvil. In Europe the drop height is only 1.5 meters. Why so low, when bicyclists frequently exceed 14 mph in forward speed?
The typical road or trail bike crash involves a drop to pavement. The important energy in that crash is supplied by gravity, not by forward speed. Although forward speed can contribute some additional energy, the main force is the attraction of gravity, and the impact severity is determined by the height of your head above the pavement when the fall begins. It is gravity that determines how fast your helmet closes with the pavement. Some of the crash energy is often "scrubbed off" by hitting first with other body parts. The typical bicycle crash impact occurs at a force level equating to about 1 meter (3 feet) of drop, or a falling speed of 10 MPH. The rider's forward speed before the crash may be considerably higher than that, but the speed of the head closing with the ground, plus a component of the forward speed, less any energy "scrubbed off" in other ways, normally average out at about 10 MPH.
So bike helmets are tested with a 2 meter (6.56 feet) drop. Motorcycle helmets are tested at 3 meters, about 17 mph. A really good bicycle helmet can handle that.
As a 2009 study shows, helmets prevent between 63 and 88 per cent of brain injuries. Those are good odds. But that means that helmets did not prevent all brain injury for 12 to 37 percent of the riders. They are optimized to prevent life-threatening catastrophic brain injury, not the milder forms of concussion. If they are softened to prevent mild concussions they will compress too fast and bottom out in the more severe impacts. Today's helmets may or may not be perfect in striking the balance, but we know they work well. Still, every bike helmet sold in the US has a sticker inside warning you that "no helmet can protect the wearer from all foreseeable impacts." That sticker is required by law.
If you have the misfortune to impact head first against a bridge abutment at the bottom of a screaming 55 mph downhill, your helmet will not prevent a head injury. That is not very important, since the rest of your body will be mush anyway. Fortunately that very seldom happens. Most of the cases where the helmet's limits are exceeded involve crashes with cars. Every rider understands that it is very important to avoid being hit by a car.
Obviously a helmet covers only your head, leaving the rest of your body unprotected.
In sum, your helmet will do a good job of protecting you in a fall, but the limits can be exceeded. It should be clear
that nothing about wearing a helmet affects the need to ride safely, or the need for safe riding facilities.