To visualize something is to be able to see it in your mind. From the twitching in their feet, it seems that sleeping dogs often visualize a fenced-in area and about 30 squirrels.
Visualizing is a lot like imagining — both involve picturing something in your mind. But while imagine has the sense of wondering and exploring, when you visualize something, your hope is to make it real. Basketball players visualize themselves making a shot to help them sink the basketball in the hoop. Visualize yourself getting the job as you're going in to be interviewed and your chances for success will increase.