Permethrin is an insect repellent, and in reasonable doses, actually kills the insects which aren't repelled. Clothing and other cloths can be treated and it will last a few washes. Some insect repelling clothing is pre-treated with it, as well as other chemicals which increase it's stability and presumably make it last longer.
For a while it was used in medical creams, for treating the likes of lice and scabies, and it will kill them. Also as an agricultural and household insecticide. In the last decade or so it's become more common in lower doses as a repellant, as DEET was shown to be damaging on many fabrics as well as for human (and animal) health.
Permethrin is fabric safe and less toxic to warm blooded animals. However, it is much MORE toxic to cold blooded animals than DEET. Fish and amphibians especially, so be careful about getting any in the water. It's also extremely toxic, strangely, to cats. That one's fairly well known because a lot of flea and tick collars for dogs are permethrin soaked, but those type are not to be used if the dog is in close contact with cats, and they're talking about actually outlawing the permethrin ones for that reason.