Doh! I can't believe you don't know what a .exe file is. It is an executable file; ie: a windows program. Not a mac program. It won't work on a mac.
Personally I filter out exe files so they don't show up in my searches. Mac files generally have hidden extensions for a start. The files you should be looking for are sit, dmg, possibly gz which are compressed files. Mac files are usually compressed for easy transport over the net. StuffIt Expander will expand sit & gz. Disk Copy will mount dmg files. Oh & Toast will mount .toast & img files & some dmg's.