Re: What's a "cow run"
If you've beaten Baal in any given difficulty setting, you can go to the Secret Cow Level in that same difficulty setting. Since you're in Nightmare, you've beaten Normal, so you can go to the Cow level in Normal.
Go to Tristram in the Stony Field, act I, and in the west corner you'll find the body of Wirt. Click it, and he'll give you some gold and his leg. Take his leg, go to the Rogue Encampment, buy a Tome of Town Portal from Akara, and put that in the Cube along with the leg. Transmute, and a red portal will open to the Cow level.
It gives you (some) experience as well as a lot of items (There's quite a few cows there..)
The reason most people do it is for jewelry (charms, rings, amulets, jewels), some runes (a lot of monsters) or socketable items (If you run without MF-gear)