Windows executables end with ".exe". They use a different format than Linux's "ELF" executables, and often call Windows-specific calls, so they will NOT run in Linux.
The Linux OS itself does not have a concept of "file extensions". Instead it uses the "executable permission", which is not part of the filename. Sometimes they they end with ".elf" (because Linux executables use the ELF format), or ".run" (to tell you that you must run it).
Each file has an owner and a group.
The file has "flags" that say separately what the owner, group, and other users can do with the file.
These permissions include "read", "write", and "execute".
If you wanted to install a program, Linux programs are not stored in self-extracting executables like in Windows.
Instead they are stores as an archive of the program's source code (the ".tar.gz" and ".tar.bz2" formats are often used) that you must compile.
Or use the distro's package manager, it will download and install precompiled programs automatically.
For example in Ubuntu:
sudo apt-get install mypackage