Since Bilam is a prophet, the text must be describing his capacity for prophetic insight – his ability to perceive with his mind’s eye.
However, the same Hebrew root can be understood as meaning closed, not opened. Some of the sages therefore thought that the Torah was telling us that Bilam was blind in one eye (since it does not say sh’tum b’einav, i.e. sh’tum in both eyes, it seems that he had a problem only with one eye).
Others said his prophetic capacity was defective until the moment when he “saw that it was right in the eyes of the Lord to bless Israel” (Num. 23:1) and when he “lifted up his eyes and saw Israel dwelling according to its tribes, the spirit of God came upon him” (Num. 23:2).
If we take this last interpretation, we learn that like all human beings Bilam does not immediately see the truth of a situation. He needs God to show him the real picture.