Marbling (aka intramuscular fat) refers to the white fat in the muscle of beef.
It is called marbling because the beef has a marbled look to it. Meats with greater fat, have greater marbling and therefore are the juicier more flavorful cuts of beef.
The USDA has a grading system for the quality of meat that is based on the age of the beef and the amount of marbling in the beef. The most common grades found commercially are Select, Choice, and Prime. With Prime being the highest or most marbled and therefore the tastiest and therefore the most expensive.
In the pictures above you can see the difference in the marbling between these two cuts of beef.