The Firefox web browser contains its own DNS cache independent of your operating system. For most users, it is quite convenient, it allows a faster web browsing as it doesn't have to request for DNS at each connection to recently visited websites.
For some users it gets in the way though and requires them to restart their browsers in order to clear it.
To disable the DNS cache:
From your browser:
Type in about:config in the address bar.
Right click on the list of Properties, select New > Integer in the Context menu
Enter network.dnsCacheExpiration as the preference name and 0 as the integer value
When disabled, Firefox will use the DNS cache provided by the OS.