The Barrel Roll is a not competition maneuver, as far as aerobatics is concerned. It was used mainly as an evasive/defensive maneuver in combat, particularly WWII. The goal is to force the attacker to overshoot the target. The idea is to shorten the distance a pilot covers in a straight line by adding lateral movement  (the distance between the pilot and the attacker). Not so much to slow the plane down, which also works, but sacrificing too much airspeed or altitude for that matter in a dogfight can mean disaster. Also the complexity of the maneuver serves to defeat the guns resolution, at least for a short time until the attacker can correct.

The barrel roll is a combination between a loop and a roll. You basically complete one loop and one roll at the same time. Externally it looks much like a corkscrew lying on a table. While still not a maneuver used in aerobatic competition, it still requires a fair amount of skill to perform well.

In a barrel roll the accelerometer will always (or should) indicate positive G forces, usually between +0.5 and 3.0 G's.

The Barrel Roll is a defensive manuever. It is a more complex manuever in that one needs to have a very good foundation in the basics, particularly the yoyo, before you can master it. The Barrel Roll is very similar to the lag roll, but it is defensive in nature. Hence it will be done with greater urgency.
The barrel roll is defensive because its goal is to force the overshoot of an attacker who is closing fast. The idea is not so much to slow your plane down in airspeed, but to shorten the distance you cover in a straight line by adding lateral movement.

Think of it this way. An attacker is closing on your six from altitude. He is traveling from point A (Your six o'clock position) to point B (a position leading your flight path at 12 o'clock). By pushing your flight path to the side in a barrel-shaped circle, you lengthen the time it takes you to travel to point B while your attacker is already closing upon point B with great speed as it is. Also the complexity of the movements is able to defeat a guns resolution in the short term.

Execute the Barrel Roll by:
To begin a barrel roll roll 45 degrees right or left and begin a shallow climb. This will create the lateral movement you'll need to begin the roll. Many make the mistake of excluding this first step and they only perform a corkscrew which is easy to gun down. You need this first step to the side to creat a larger, barrel shaped, circle.

The next step is to roll back the opposite direction 90 degrees and pull again. So if you rolled 45 to the right and pulled up into the start of a yoyo, you then roll 90 degrees (45 until you are level, and 45 more to get set for a left yoyo) and pull (just like a yoyo) in the opposite direction. You will not need to be anywhere near a stall as you want to conserve energy for a kill (Step 4 below). If you did Step 1 correctly you won't have to work that hard at this.

Then you may watch for the overshoot. The attacker should shoot by like a seed being squeezed out of a grape! To begin with you will move him from your dead six view to your six high view and finally to your straight up view. Once he is in the straight up view, you have them. This is also your lift vector, and any time a plane gets in front of that you are moving over to the offensive. Rotate around your enemy simply by using the straight up view. Rotate so that you are rolling toward his flight path.

When he moves out of the up view to a more forward view, shoot the fool.