According to the dictionary, rennin is defined as "a coagulating enzyme that can curdle milk, found in rennet."
The functions of rennin enzymes are explained in great detail at Vivo. Colorado State.edu. For those who want to understand the function in laymens terms, however, it is pretty simple to understand the function of enzymes: Rennin enzymes are the enzymes that curdle milk as a part of the digestive process.
In many animals rennin exists, if at all, only for a limited period of time shortly following birth. Animals that lack rennin or chymosin enzymes in their bodies (like humans) may still be able to coagulate milk, however, without this rennin. In this case, the coagulation occurs as a result of pepsin, which replaces those rennins. Pepsin is stomach acid that is produced naturally in animals and individuals that do not have multiple stomachs.
The process of using rennin (or a commercial version of rennin that is commonly known to the cheese producing industry as rennet) is used to create certain kinds of cheeses that are prized for their unique flavor among the gourmet cheese market. These types of cheeses have been converted to casein through the enzymatic process as opposed to through chemical means.