Our Immune system shows different types of responses depending upon the infection or disease.
In Cell-mediated immunity, as the name suggests the immune system of the body makes use of certain cells like Natural Killer (NK) cells, Phagocytes (by a process called as Phagocytosis) and more specifically the T-cells or T Lymphocytes, to fight against foreign particles. In such an immunity response, specific body cells identify foreign bodies and whole of the foreign body is engulfed or destroyed. Alternatively chemical substances are produced that fight against the pathogens. A subclass of T cells, then, bears a memory of this encounter, which is very helpful when the body meets the same pathogen again. This is in fact the basis of vaccination.
In Humoral ("Humoral" means body fluids like plasma, lymph) immunity, however, the body cells do not combat the infection directly as in the cell-mediated type. Instead certain cells like B cells or B Lymphocytes (which are in turn activated by T cells) produce antibodies in response to the foreign antigens. The antibodies then bind to these antigens, destroy them and thus prevent our body from infections.