to look intently: to fix the eyes or the attention on something with real interest, not a passing glance
At its core this word is not just to see but to look hard at, to turn the eyes toward something and hold them there. Where the ordinary word for seeing reports what happens to fall in view, this verb is deliberate. It is the looking of someone who scans the horizon for rain, who counts the stars one by one, or who locks eyes on a person and weighs what is there.
Because looking this closely is always an act of the will, the word carries far beyond the eyes. Who or what a person fastens their gaze on says what they care about, hope for, or trust. So the Bible uses it for turning to God for help, for God turning his attention toward a sufferer in mercy, for staring at evil one cannot stop, and for the steady contemplation of God's words and works. The senses below are not different words but the same intent look aimed in different directions and with different feeling.
The disposition behind the look is supplied by the situation, not by the verb itself. The same form means tender regard when God does it to the afflicted and powerless complaint when a prophet says God seems to be watching wrongdoing and doing nothing. The reader has to ask not only that someone looks but where they look and with what heart.