"explorer.exe" is the process for Windows desktop. It is a base process for all applications running within Windows and a process which Windows cannot run properly without.
"iexplore.exe" is the process for Internet Explorer, the default browser in which Windows surfs the internet. Below are only three possible answer's to why there could be two.
2: If you have upgraded Internet Explorer to version 8 (Any Beta or RC), then you should be aware that the new browser uses a seperate process of "iexplore.exe" for each tab currently open. If you start your browser, you will automatically have two processes, one for the main browser window and another for the first tab.
Microsoft has implemented this technique into Internet Explorer 8 to accomodate a more effective process priority to each tab. An example would be if you were listening to streaming radio in one tab and surfing in another. The tab which has your focus can and will take priority over the background tab and cause the radio to cutout or even stop. In the new Internet Explorer, each tab has its own process which allows equal priority over CPU time and will not let another tab steal the processing time from any other background tab.
3: If you do not have Internet Explorer version 8, then the most assured answer is that you have a form of adware/malware. You can test this if you go into your task manager and try to end all of the "iexplore.exe" processes and if they manage to return without you opening Internet Explorer or if two open simultaneously when you do (If there are no Pop-Ups).
This is potentially a very serious form of malware. It can steal personal banking and other information, cause numerous performance hinderance's as well as redirecting you to spam websites and causing numerous pop-ups.
Get an adware/malware scanner (I suggest Malwarebytes) and perform an updated scan of your entire computer to remove these threats.