I wan't to create a Wiki for our company which has several product requiring their own Wiki. Is it possible to create subwikis with MediaWiki? If so, how?
No, this is not possible within MediaWiki. The closest you would get is using custom namespaces (http://www.mediawiki.org/wiki/Manual:Using_custom_namespaces).
Commercial enterprise products like Confluence do offer this functionality.
If you want to keep it free you could create multiple MediaWiki instances. MediaWiki setup is not terribly complex and can easily be scripted to set up multiple instances using multiple databases and Apache VirtualHosts.