It's essentially a brush-on primer, but can be thinned for airbrushing.
Its main purpose, like any other primer, is to prep a surface for paint. It is used to fill things like sanding marks, scratches etc. Brushed on thinly, it will self-level and the brush streaks disappear.
For larger defects, eg. filling ejector pin marks, it can be applied using a toothpick and sanded smooth when dry. It does shrink as it dries so it may require several applications. I often fill pin marks using this stuff. Apply a drop of LSP in the recessed pin mark using a toothpick and run the tip around the edge of the pin mark to ensure it's filled to the edge. Overfill it so that it forms a raised dome over the pin mark. When fully dry (if you use it this way it may take several hours to harden), use a chisel-edge knife and shave it off flush with the surrounding surface. A few swipes with a piece of wet n dry and you have a perfectly filled pin mark.
It can also be brushed on in multiple layers to re-contour mis-shapen parts. It sands easily and feathers very nicely. Brush on, allow to dry, repeat, until the part is shaped as required.
If you fill using a regular putty, you can often see this under a coat of paint because the putty is more porous than the surrounding styrene. You can use LSP to "spot prime" over the putty to reduce this effect.