What kind of a nut is this holding my front wheels?
It's called an axle nut in bicycling parlance. In general terms, it's a type of flange nut.

Like most things bicycling, there's little standardization of these. The most useful reference is here at Park Tool's site. 

It could be a 5/16 inch x 24 tpi, 3/8 inch x 24 tpi or 8mm x 1mm. Or some weird other variant. The likelihood of finding the right one at a hardware store is low and you might accidentally jam or cross-thread it if you force it. For example, some axle nuts are 26tpi which will thread part way then jam.

Your local bike shop will likely have a big box of old axle nuts that you can sort through. If they don't, find an bike shop that is older and dirtier. The less teeth the mechanics have (both oral and on their steeds), the better.