Underlay is the cheapest way to make a carpet feel expensive.
It softens the floor, it insulates against cold coming up from below, it deadens sound between floors, and it takes a lot of the wear that would otherwise go into the carpet itself. A mid-range carpet on good underlay will feel and last better than an expensive carpet on cheap underlay.
There's a range of thicknesses and densities and they suit different rooms. A thick, soft underlay is lovely in a bedroom and wrong on a staircase, where you want something denser and more stable underfoot. If you've got underfloor heating you need a low-tog underlay, or the heat stays under the floor where it's no use to anybody.
We'll recommend what suits the room and the carpet.