A person is finite. The mind is contained within the brain, and the brain is obviously finite. But a person, like just about anything that you can look at, expands in complexity the closer you look at him. A person is finite, and therefor understandable, but that finite space is so large that it might as well go on forever.
As far as understanding other people goes, there are certain limits of diminishing returns. That's why when we get to know other people, we want to figure out the broad strokes first, to trace out the shape of them without knowing the color, texture, and sensation of their being. That, of course, depends on what you want from other people - sometimes we crave only the sensation without the context, a sort of abstract art of knowing someone. But while building a verisimilitudinous version of another person in our head, there comes a point where each additional detail adds relatively little to the picture. That's the point when we think we know them.
Infinity is boring. The mundane details of a life are boring. I think there must be some sort of sorting algorithm of interest, and it's my guess that the more interesting things are the ones that happen least often, or the ones that make the most impact - the outliers of life. Me eating blueberry Pop-Tarts during my morning shift in the Science Commons lab at St. Scholastica is boring, because it happens three days a week. But at the same time, it can fill in part of the map of understanding. If you knew only that about me, you would be able to infer a great number of facts from it.
I tend to view people through metaphors. A person is a tree, with the important information in the trunk and the mindless details in the leaves. A person is a painting, my picture of them being painted and repainted with ever greater detail. A person is a function, whose variables I'm finding out to ever more exacting precision.