Normal, "non-super" antigens activate T-cells in the following manner: they are first engulfed and processed by a professional antigen presenting cell (APC), e.g., a macrophage. The processed antigen is then presented along with an MHC class II molecule on the surface of this cell. The T-cell's T Cell Receptor (TCR) then binds this complex; it must be able to recognize both the MHC class II and the antigen, and in addition to this "main signal" other co-simulatory signals are also needed. The important thing to remember is that a T-cell will only react to a specific antigen it's specific with when it's present with an MHC class II molecule it can recognize. This is known as MHC restriction
A person has 3 genes (each having 2 alleles,for a total of 6 alleles) for MHC class I: HLA A, B and C, and 3 genes for MHC class II: HLA DR, DQ and DP. These alleles are highly polymorphic, i.e., varied, with each of these 6 genes having hundreds or thousands of different alleles, and the combination of alleles differs from individual to individual; it's very unlikely that two people who aren't identical twins would have the same combination of HLA alleles.
MHC molecules can only bind peptides, and in addition, they cant bind ALL peptides; of all the peptides that can possibly be bound by an MHC molecule, a particular MHC molecule can only bind a select number of those peptides. Different MHC molecular forms, be they class I or II, can bind, and thus present, a different set of peptides. Having different HLA alleles at your immune system's disposal means there's a larger pool of possible peptides your APCs can present with the different MHC class II isoforms they have, allowing defense against a larger pool of antigens.
A normal antigen has 2 "restrictions" on its ability to activate a T-cell clone: it must be presented by an MHC class II isoform that can bind it, and it must be recognized by a T-cell with a compatible TCR.
Superantigens activate T-cells in an unconventional manner: They have a domain that binds to the TCR, though not at the usual antigen binding site, and a domain that binds to the MHC class II molecule, but not in the usual peptide-binding site these molecules possess. Since it binds outside of these regions that are specific to particular molecules, they're not restricted by the antigen specificity of the TCR nor are they restricted by the MHC class II isoform they're utilizing. Hence why, even if they do need MHC class II-positive cells to be able to activate a T-cell clone, they're not MHC-restricted.