Dr. Rao has answered the question in a nutshell, but allow me to elaborate a bit. The primary reason why the webmasters choose to hide the extensions from the URLs is to hide the underlying technology from hackers and other possible malicious attackers. For example, if a page ends with .html or .aspx, it is easy to find out exactly what (HTML/XHTML and DotNET) were used to develop the concerned website.
In addition to points #1 and #2 mentioned by Dr. Rao above, the extension does not actually convey any sense or meaning to most of the users. Since modern web-developing is highly user-oriented, it is advised that the extension is removed from the URL structure.
Also, let me add something to Dr. Rao's fifth point a bit. If you do not include the extension in the URL, you are saving the space for four or five characters, which may be otherwise utilized. For example, the search snippet in the Search Engine Result Page (SERP) usually shows 64 characters, beyond which it is truncated and does not look good. It is, therefore, a piece of standard SEO advice to keep your URLs within 64 characters (with exceptions, though). The limit is really quite short, you see, and there is no point in reducing it further. Instead of wasting four or five characters in the URLs by writing the extension, you can add yet another meaningful keyword while keeping within the usually prescribed limit of 64 characters.