For most of our genes, we report on single nucleotide polymorphisms (SNPs), these are essentially changes at one position in that gene that cause the effect. So for these genes, we report on which nucleotide you have at that position- A,C, T,or G (you might also see D for deletion).
For the HLA genes, the varieties that can be tested for change at a lot of positions. Therefore, it makes more sense to name the whole protein that is produced, rather than the individual nucleotides.
So HLA is the gene that is being tested for, and DQ classifies which variant is produced by that gene.
Some DQ variants are much more common in Coeliac sufferers than others, and this is what the Coeliac risk score is based on.