Gina, the tests you mention and what they are probably looking for are as follows;
FBC = Full Blood Count. Conventionally a measure of the quantity and morphology of the red blood cells (oxygen carrying cells, so checking for anaemia etc), the number and ratio of the types of white blood cells (principally the infection fighting cells, can be raised in all sorts of disease states), and the number and size of platelets. (used in clotting)
ESR - Erythrocyte Sedimentation Rate. This is a broad screening test principally looking for inflammatory disease states. The higher the result, the more likely it is that a disease state is present.
CRP = C-Reactive Protein. A measure of a particular protein, produced in the liver, that is present in serum during acute inflammation or infection. Again, it is a non specific test, like the ESR, but has a different "decay" rate, so having the results of both an ESR and a CRP can be helpful.
I would guess they are looking for the presence or absence of evidence of an inflammatory episode for example infection or possible onset of something such as rheumatoid arthritis. There is some linkage to suggest that elevated CRP levels may be associated with some heart conditions also.