What is enzyme modified butter fat?
What is enzyme-modifed butterfat?
According to the United States Food and Drug Administration:

(a) Enzyme-modified refined beef fat, enzyme-modified butterfat, and enzyme-modified steam-rendered chicken fat are prepared from refined beef fat; butterfat or milkfat; and steam-rendered chicken fat, respectively, with enzymes that are generally recognized as safe (GRAS). Enzyme-modified milk powder may be prepared with GRAS enzymes from reconstituted milk powder, whole milk, condensed or concentrated whole milk, evaporated milk, or milk powder. The lipolysis is maintained at a temperature that is optimal for the action of the enzyme until appropriate acid development is attained. The enzymes are then inactivated. The resulting product is concentrated or dried.

https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/CFRSearch.cfm?fr=184.1287
That probably doesn't offer much that you don't already know.  It says that enzymne-modified butterfat is made from butterfat or milkfat and enzymes, which are themselves derived from dairy products.
What is an enzyme?
An enzyme is a protein that acts as a catalyst, accelerating chemical reactions.

Enzymes accelerate the rates of such reactions by well over a million-fold, so reactions that would take years in the absence of catalysis can occur in fractions of seconds if catalyzed by the appropriate enzyme. Cells contain thousands of different enzymes, and their activities determine which of the many possible chemical reactions actually take place within the cell.

https://www.ncbi.nlm.nih.gov/books/NBK9921/
Like all catalysts, they are not consumed or changed by the reaction they facilitate.
Should there be enzymes in my food?
Yes! As stated above, cells contain thousands of enzymes, so there's no avoiding them.  But most of those enzymes are not doing anything interesting in your food.  However, sometimes we need specific enzymes to make the food we eat.  For instance, in order to make cheese, we need to add rennet.  Rennet is a group of enzymes, including, most importantly, chymosin, which is the enzyme that causes the milk to curdle.  Some cheese also relies on the enzyme lipase, which causes fat to break down and release fatty acids.  These fatty acids are partly responsible for the flavor (and texture) of most blue cheeses, feta cheese and others.
How do enzymes enhance flavor?
To avoid a long discussion of what flavor is, let's just say that it has to do with your nose and mouth reacting to certain compounds in a food.  As discussed above, enzymes can catalyze the reactions that produce flavorful compounds.  They can also produce compounds that make already present flavors more noticeable (like how adding salt to food not only makes it taste salty, but also brings out the other flavors).
Examples
DuPont, an American chemicals company, makes a variety of enzymes that can be used to improve cheese flavor and make it easier to produce.  For example, KM450 Lipase is supposed to reduce bitterness, reduce ripening time and modify the flavor intensity of mature goat cheese.  Savorase® ARP is meant to improve the flavor of Swiss or Italian-type enzyme modified cheese, while Savorase® CHC is to be used for Cheddar flavor enzyme modified cheese.
https://www.dupontnutritionandbiosciences.com/products/natural-flavor-enzymes.html