A plastic stick with a flat, plastic grate on the end that's used to kill flies.

But why not simply use a tissue like when killing other bugs? Why do flies need a special weapon all to themselves?
Because flies are fast little buggers and most people aren't as nimble as Mr. Miyagi.

You can purchase designer fly swatters at your local dollar store that come with nifty shit on the end like a hand, a fly or a dick.

Try not to touch the end of your fly swatter. It probably has nasty bug bits all over it.

See also:
Electric Fly Swatter

For alternate spelling, see flyswatter.