Bondage suspension has nothing to do with the suspensions from hooks that are part of the body modification culture. Bondage suspension forms part of BDSM practice, and is where a person is tied or bound, and then suspended in the air from these bindings. The most commonly seen bondage suspensions are those using Shibari.
Bondage suspension is best practiced with someone experienced and by using the proper equipment. When using rope, it is important that the correct sort of rope is used (often made out of hemp) that is strong enough to hold the weight, and won't tighten and restrict bloodflow dangerously when weight is applied. It is also important that the body's weight is spread safely. If cuffs are to be used, they need to be designed especially for the purpose; standard cuffs used for restraint will not be comfortable, and may restrict bloodflow or even break when weight is applied.
The positions possible for bondage suspensions are extremely varied, though many of them are painful and can only safely be maintained for a few minutes.