to keep watch: to fix one's eyes on something with alert, purposeful attention
At its core this verb pictures a person whose eyes are trained outward on purpose. The most vivid picture is the sentry: a lookout posted on a wall, a rooftop, or a hilltop, straining to spot who or what is approaching so he can raise the alarm in time. From that concrete image the word stretches in two natural directions.
In one direction it becomes plain watchful observation: keeping something or someone under a steady, knowing gaze. God's own eyes watch over the whole earth and take in everything people do; a careful woman keeps a watchful eye over her household; and, more darkly, an enemy keeps the innocent under surveillance, waiting for the chance to strike. The eyes are open and nothing escapes them.
In the other direction it becomes expectant looking: not scanning for danger but watching for something one hopes will come. A person prays and then watches for the answer, the way a lookout watches the road for a messenger. This is the language of hope holding its breath, still eyes fixed on the horizon while waiting for God, or for rescue, to appear.
Running through all of these is the same posture: eyes deliberately fixed and holding, whether to guard, to survey, or to wait in hope. The senses below sort the occurrences by which of these the writer has in view.