Now at @V_and_A, its significance lies in the fact that it is the earliest dated (946AH/1539-40AD) carpet that we know of. Its size is impressive, but it's really the intricacy of the design which makes it remarkable. More here: http://collections.vam.ac.uk/item/O54307/the-ardabil-carpet-carpet-unknown/
The story of how it ended up in the V&A has been discussed by Moya Carey in her book 'Persian Art'. It was bought by the museum from the art import firm Vincent J. Robinson & Co in 1893. Robinson had bought it from Ziegler's, who had bought it from the Ardabil shrine in 1888.