Weight belts are used to secure dive weights around your waste. Generally you will be wearing a wetsuit while spearfishing. Wetsuits often consist of neoprene which is an extremely buoyant material and you would be unable to dive deep without weights on your weight belt.
Weight belts are made of webbing or rubber. Rubber weight belts are higher quality and more practical for spearfishing as they won't slide around. It is a good idea to invest in a rubber weight belt with a stainless steel buckle as it will last and is the most practical option for spearfishers.