explorer.exe definition, relationships, removal:

explorer.exe is an executable file that is responsible for launching parasites, loading main components of malicious programs and running a destructive payload. It is a significant part of a dangerous parasite, but can also function as a stand-alone threat. DO NOT run this file!
The explorer.exe file is installed and used by browser hijacker CoolWebSearch.time, keylogger DlDer, worm W32.HLLW.Cult.H, worm W32.HLLW.Gaobot.AZ, worm Explorer Worm.
You are highly advised to scan the system, delete executable explorer.exe and terminate all the processes it started.
Please note that the explorer.exe file actually may be a fully legitimate part of the operating system or legitimate software. Often parasites use files with unsuspicious names, but malicious functionality. You should always carefully check the file before deleting it. It may not be related with malware, but can be required by your essential programs to work properly.