In the twentieth century, biologists learned to treat plant tissues with the natural product colchicine. The action of this drug on the dividing cells of actively growing tissue prevents the cell from completing the process of cell division, but only after the original diploid set of chromosomes has been duplicated.
The resulting plant cells, in the case of our diploid daylilies, now have two sets of 11 pairs of chromosomes, for a total of 44 chromosomes in all. The word "tetraploid" was coined to descibe this new condition -- it means, roughly, having four sets chromosomes.
The tetraploids were considered to be bigger and more robust than their diploid forms, but that need not be the case for every tetraploid compared to every diploid. Indeed, the effects of extensive breeding have long since overwhelmed the simple effects of the chromosome doubling.