WoW64 stands for Windows 32-bit on Windows 64-bit. SysWoW64 process running in your Windows is part of your Windows operating system. There are many Malware and Virus remover sites which claim it to be a Malware or Trojan Horse and tries to sell their Paid Anti-Virus, Trojan Remover tools.
In Windows folder, System32 directory is reserved for 64-bit applications. When 64-bit versions of the DLLs were created, most DLL file names were not changed. 32-bit version DLLs are now stored in a different directory. File system redirector is used by WOW64 to hide this difference.
When a 32-bit application makes an attempt to access %windir%System32, the access is redirected to %windir%SysWOW64. And %windir%lastgoodsystem32 is redirected to %windir%lastgoodSysWOW64. Access to %windir%regedit.exe is redirected to %windir%SysWOW64regedit.exe.
SysWOW64 folder contains several applications to support 32-bit applications e.g. cmd.exe, to register 32bit windows services, odbcad32.exe, to register ODBC connections for 32-bit applications.
16-bit applications made for MS-DOS and early versions of Windows are normally not compatible with 64-bit Windows Vista, 7 and 8. 32-bit version of Windows XP, Vista, 7, and 8 can run run 16-bit applications easily.
Both 32-bit and a 64-bit version of Internet Explorer is found in Windows because of large number of 32-bit ActiveX components available on the Internet which can not run on 64-bit version. 32-bit IE is used by default and 64-bit IE can not be used as default web browser.