First of all MHC stands for major histocompatibility complex. There are two types of MHC.
MHC type one is present on all of our cells with a nucleus. The purpose of these protein complexes is called antigen presentation. T-cells cannot recognize free antigens on their own, it has to be presented to them in the proper way. This is what these proteins do. In every cell there are lots and lots of proteins, that get digested to small polypeptides (short aminoacid sequences) by proteases during the natural recycling process. The cell takes a small portion of these polypeptides and presents them on its surface through MHC I complexes, that the immune system can read. This is like the cell saying to the immune syytem that "hey I got these proteins in me". Now if the cell is infected (by a virus most likely) then the "attacker's" proteins get digested and presented as well and its like saying " hey I'm infected and the attacker has these proteins".
MHC II serves similar function but it is only present on professional antigen presenting cells (APCs). These complexes present peptides derived from proteins consumed and digested through phagocytosis or receptor mediated endocytosis. It's like saying "hey we got a larger attacker and it has these proteins"
So, long story short T-cells cannot recognise antigens on their own it needs to be presented to them on MHC complexes and then and only then can they be activated.
Edit: A list of useful articles in the topic of antigen processing / presentation for further details:
January 14, 1998 14:59 Annual Reviews AR052-12
Annu. Rev. Immunol. 1998. 16:323–58
MECHANISMS OF MHC CLASS I–RESTRICTED ANTIGEN
PROCESSING Eric Pamer and Peter Cresswell
Cell, Vol. 76, 287-299, January 28, 1994.
MHC-Dependent Antigen Processing and Peptide Presentation: Providing
Ligands for T Lymphocyte Activation
Terry Y Nakagawa, Alexaiider Y Kudensky
The role of lysosomal proteinases in MHC class Il-mediated antigen processing
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and the wiki page :)