The FBI technique involves holding the flashlight in your weak hand and holding it above your head and to the left or right at the full extension of your arm.

Think of the Statue of Liberty and imagine that instead of a torch in her upraised hand that she has a flashlight and that instead of a tablet in her other hand she's instead pointing a handgun at eye level and you've pretty much got it.

Strengths

The FBI technique allows you to sometimes get a light behind objects so you can't get a light behind any other way.

It's also a very free technique, meaning that if for some reason you need to radically alter the orientation of the light you can very easily move it around to the position you need.

One of the oft-stated advantages of the FBI technique is that if the light is up and away from your body if someone shoots at the light they will be missing you.

This is of dubious value, in my opinion, because while there are some guys who will probably take dead aim at the light and shoot it, most will simply shoot in the general direction of the light.

Weaknesses

The FBI technique is one of the most difficult techniques for indexing the light and the sights of the weapon together, in my opinion.

It is also easy to end up backlighting yourself using this technique if you aren't careful because a fair chunk of your body is in front of the light source.

It also assures that if you have to shoot you will be doing so with one hand, and one handed shooting is no small task under stress in low light.