"The Torchwood website" is a term with two principal meanings, owing to ambiguity about the word Torchwood.
Its primary meaning is "the site hosted at http://bbc.co.uk/torchwood". That is, the "Torchwood website" is the real world site for the television series, Torchwood. This site has been active since the British premiere of series 1.
However, early in the show's run, there was another site hosted at http://www.torchwood.org. This site was the fictional, in-universe website of Torchwood Three, the branch of Torchwood depicted in the series Torchwood. During series 1, the site offered a virtual tour of the Hub, case files and character biographies of the team. This content was replaced by the interactive Torchwood Mission Game during the British broadcast of series 2. The Torchwood fictional website was not updated past series 2 for series 3 or series 4.
The distinction between these two sites was blurred further when torchwood.org was simply redirected to bbc.co.uk/torchwood, where the series 2 content of torchwood.org continued to reside, at least in part.