A soap flower is a petal moulded from soap, assembled into a bloom and usually arranged as a bouquet or set in a gift box. They are given as flowers rather than used as soap, and they last indefinitely, which is the whole point of them.
Yes, they are actually soap
Usually a glycerine or palm-based soap, moulded very thin and dyed. You can peel off a single petal and wash your hands with it, and it lathers perfectly well. Most people never do, because the object is the gift and dismantling it defeats the purpose.
If someone does want to use them, one petal per wash is plenty — they are thin and they go quickly once wet.
Why they last and when they do not
Kept dry, a soap flower lasts for years. The two things that ruin them are humidity and sunlight. In a steamy bathroom the petals soften and begin to fuse into each other, which cannot be undone. In direct sun the dyes fade, and pinks and purples go first.
So a bedroom shelf or a hallway is right, and the windowsill above the bath is exactly wrong, which is unfortunately where they usually end up.
Scent
Fragrance is added to the soap base and it does fade — noticeably over six months to a year, depending on how the flowers are stored. A boxed set that stays closed keeps its scent far longer than an open bouquet. Nobody selling these mentions it; it is worth knowing before you buy one as a keepsake and expect it to smell the same in two years.
Bouquets and boxes
A wrapped bouquet reads as flowers and photographs like flowers, which is what makes it work as a gift for someone who would rather not watch real ones die. A boxed set reads as a gift set and travels much better in the post — bouquet wrapping crushes.
If it is going in a parcel, choose the box.
Who they suit
The obvious answer is anyone who likes flowers, but the genuinely good use is for people who cannot have fresh ones: hay fever, cats, hospital wards where cut flowers are not allowed, or a desk with nowhere to put a vase.