Why did he use the specific word "uncovered"? It's obvious from his immediate change of orders and rapid movement it means exposed or revealed to the enemy, but why the word "uncovered".
I therefore determined to move swiftly towards Jackson, destroy or drive any force in that direction and then turn upon Pemberton. But by moving against Jackson, I uncovered my own communication. So I finally decided to have none--to cut loose altogether from my base and move my whole force eastward. I then had no fears for my communications, and if I moved quickly enough could turn upon Pemberton before he could attack me in the rear.
Accordingly, all previous orders given during the day for movements on the 13th were annulled by new ones.
ed: I added the paragraph
ed2: the whole book is here http://www.gutenberg.org/files/4367/4367-h/4367-h.htm
Cover means protection. In military context, cover means protection from some form of attack. To "uncover" is to remove protection.
In context, Grant was deliberately exposing his logistics/communications train by removing the protective troops.