The recognition of the abnormal cell by the NK cell is made possible due to a balance between the signals induced by inhibiting and activating receptors:

A : Inhibiting receptors (discovered by Klas Kärre) recognize MHC class I molecules present on the surface of all normal cells (with the exception of spermatozoids). They enable “self” recognition by the immune system and present antigens to cytotoxic T lymphocytes. The inhibiting receptors block the lysing process independently of the antigen presented and therefore protect the normal cells from destruction by NK cells.
B : The activating receptors bind to molecules which resemble MHC class I molecules but which are expressed after cellular stress such as tumor transformation or infection. These receptors activate the lysing process if this signal is sufficiently strong to remove the inhibition caused by the inhibiting receptors.
C : In order to avoid recognition by the T lymphocytes, tumor or infected cells do not express any more (or less) MHC class I molecules, but they are equally sensitive to attack by NK cells which will no longer be inhibited by their inhibiting receptors.

These class I MHC molecules could also be behind a form of NK cell education. “For example, studies with mice deficient for some MHC showed that NK lymphocytes were not able to respond to tumor cells, suggesting that without a "self" recognition precondition, NK cells can not be activated ” explains Nathalie Jacobs

Killers of cancer and  a lot more besides

Although NK cells have been studied for a shorter time than T lymphocytes, their efficiency against tumor cells no longer needs to be proven. For example, it has been shown that people whose NK cells were less efficient at destroying tumor cells in a laboratory test had a higher risk of developing cancer. In addition to their role of defense against tumor cells, NK cells are also likely to attack cells infected by a virus. “Several studies have suggested  an important role played by NK cells in the control of HIV infection (editor’s note: the virus responsible for AIDS). For example, people called ‘elite controllers’ (infected by the virus but not having developed the disease) had NK cells with a greater cytotoxic activity than people who were not able to cope with HIV infection”. Finally, NK cells also support the adaptive immune response by stimulating antigen presenting cells and by secreting cytokines which activate T lymphocytes.