In some ways, receptors are like the address labels of biological systems - they allow communications from other cells, and even other organisms, to figure out where they need to go. There are huge numbers of biological processes that are mediated by the action of receptors - everything from the effects of estrogen in the body to recognition of foreign bacteria.
Not all receptors, however, are present on cell surfaces. Receptors are important for multiple types of cell signaling - not just between cells, but within a single cell as well. That's why some receptors are found inside a cell's cytoplasm; they regulate cell processes from there.
People often discuss specific cell receptors when they are talking about HIV infection. Most strains of HIV gain entry to white blood cells through a receptor known as CCR5, and mutations in that receptor are known to affect resistance to HIV infection.