This is an important topic in immunology, especially for vaccine development.
MHC or HLA is a molecule expressed by some cells of the immune system which acts like a "catcher's mitt" and "presents" short snippets of protein to other immune cells. Other molecules act alongside MHC to provide co-signals which promote or suppress immune attack against the peptides that MHC presents.
Basically, it's a protein that holds out chunks of other proteins in order to educate the rest of the immune system. Here's the catch: different people have different genes for MHC which do a better or worse job of presenting certain peptides. This is one reason why different people can respond to different vaccines or different pathogens or cancers: they have different MHCs which may or may not present peptides from the relevant targets.
Thus, one big challenge in medicine right now is to develop good models for which peptides are best to include in a vaccine. The right answer depends on the genetics of the vaccine target (ebola, a tumor, e. coli etc) and also on the genetics of the person being vaccinated (does this person's MHC gene properly present this vaccine?)
So, to datafy this, people sometimes make arrays which allow us to quantify which peptides bind to which MHC genes in high throughput. Then we can use that data to learn which factors are most important for P:MHC binding. "MHC restricted" means that we are talking about a specific genetic subtype of these molecules.
Hope that helps.
Bion Alex Howard