A swath was originally the long narrow space created by a single swing of a scythe in a field of grass or corn as the cutter moved through it. Nowadays it is used much more figuratively to mean any broad strip of land.
The figurative use of swath also has nonphysical senses as well, as in the term "a significant swath of the population believes..." Or if someone is trying to attract attention to themselves, or is making quite a public stir, they might be said to be "cutting a swath through the business world" or "cutting a swath on the dance floor." Hopefully, neither of the latter involves using scythes.
