In the news, you will quite frequently hear about a "controlled explosion", especially in connection with "suspicious packages" and other fears of terrorism. However, it is only very rarely explained what one of those controlled explosions actually does, nor how it is planned or executed.
How bombs work
Anyone who has ever seen a thriller film, will have seen a couple of sticks of dynamite, a huge, visible timer, and a red, blue, and green wire. In real life, however, a bomb-builder would never make such a device. A serious, self-respecting terrorist will create a device that is as simple as possible, but also tamper-resistant, through using a motion sensor (which sets off the bomb in case of a change in acceleration (G-force) such as being picked up), a pickup switch (A physical switch that gets activated if the device gets moved), a power loop (that sets off the device if the power from the main battery is cut - the classical "red wire, blue wire" thing you see in films) or a combination of the above. Particularly serious terrorists might use a proximity or light sensors, and would definitely use duct tape or similar around the entire device to make sure that none of the actual mechanics are visible.
Most non-suicide-bomber explosive devices will be either on a remote controller or a timer - or a combination of both. When a terrorist wants to set off the device, they can do so via a pager or a mobile telephone. The advantage of this - for the terrorist - is that the device can be detonated from anywhere in the world. Other forms of remote controlling can be done with radio signals (such as used in remote controlled planes etc) etc. Timed devices can be set to go off at a particular time (like an alarm clock) or after a particular time (countdown timers). If a timed device is used, however, the terrorists will almost certainly disable any read-out: There is no way they are going to give the anti-bomb-squad the benefit of being able to see how much time they have to defuse the device.
How a controlled explosion works
The first port of call for the police or army bomb squad is to see if they can defuse the bomb. This is often done by a remote-controlled robot, who will try to remove or disconnect either the ignition system (this might be a primer charge such as a blast cap) or the timing / remote control device. The remote-controlled robot can have a series of cameras (infra-red, colour, etc), sensors (geiger-counters, swab sensors etc, to find out what the explosive device consists of) and remote-controllable tools etc.
If the defusing succeeds, the device might still be dangerous, in case the terrorists have installed secondary detonation devices, such as movement sensors etc. If the defusing fails, even more danger is present. In both cases, the bomb experts will want to conduct a controlled explosion.
"Controlled explosions" is not actually an overly precise term, as explosions can be extremely difficult to control, because they - well... they explode. The "controlled" part, then, describes the act of controlling one or more aspects of an impending explosion.
One of the aspects that can be controlled is the timing. Some of the remote controlled robots can be fitted with a shotgun, and shooting at the explosive device is a form of controlled explosion. Especially when dealing with high-explosives, shooting at the actual detonation mechanism might actually disrupt the explosive device, meaning that while the primer charge might go off, the main (and most dangerous charge) might not go off. The "controlled" element of this type of explosion is the timing: Because the bombs squad know when they are planning to shoot the device, they can make sure that all civilians are out of the area at the time of the potential explosion, which would minimise casualties.
Another aspect that can be controlled in some cases, is location. If the bomb is suspected to be inside a van parked next to a structural pillar of a large building, for example, they can move the actual van away from the hot-spot which would cause the most damage. If the bomb is in a bag or hold-all, using a remote-controlled robot to move the bag away from a high-risk area (such as in the basement of a building) into a lower-risk area.
In other cases, a controlled explosion can be done by putting a second explosive device next to the suspected bomb. The bomb squad can then place a heavy, damping material around the area, and set off the secondary device. The hope is that the secondary device will either disable the main bomb without setting it off, or set it off, and hope that the explosion will do only minimal damage.
In a final scenario, a heavy metal shield can be used to deflect the explosive force away from sensitive areas.
Often, bomb squads will use a combination of two or more of the techniques above. If a controlled explosion has to be used, damage is unavoidable, but the idea is to limit the damage and eliminate the loss of life as far as possible.
See also Timer and Motion Detonator