On a simplistic level, physically the experience is a feeling of pulling, burning, and pain all jumbled up, but for most people this physical aspect is "tuned out" very quickly.Although individual experiences differ greatly, ultimately the act of suspension can be an euphoric floating sensation. On one end of the spectrum you find people that enter a trance like state, feeling no pain whatsoever, and on the other end you find people that experience extreme pain, nausea and panic attacks. In general, most people enter a shock-induced state of disorientation spiked with moments of pain and euphoria. In laymen's terms, the act of suspension causes the body/mind to enter a state of shock while being physically positioned and restrained in a "floating" state.
There are some general commonalties expressed by most suspendees, such as the feeling of intense tugging which gives way to a more relaxed sensation as the body leaves the ground. However, the varied motivations for suspending make it such that different people have different experiences. As with much of life, you get out of it what you put into and your expectations will often become self-fulfilling prophecies. Some people find it boring, others are changed forever, and some don't ever even think about it beyond simply performing the act. Many find that good or bad, it is not what they expected.
Many people feel intensely at peace while suspended; an experience of complete surrender. They enter a state of hyperawareness and deep trust in themselves and the universe. Almost everyone agrees that the hooks are painful, but some people find the sensation of tension on the skin moving and inspiring.
For some people the experience is much lighter; they just want to try it, and when they do they get no emotional release and find themselves giggling and smiling and instead just enjoying the feeling of "flying".