repeatability, distinctiveness, and locality
The three properties a keypoint must have at once -- findable again, tellable apart from its surroundings, and pinned to an exact spot.
A good keypoint must pass three separate tests at once. Repeatability: the same physical point gets detected again in a second image of the same scene, even after a small change in viewpoint, scale, or lighting. Distinctiveness: the point's local neighborhood looks different enough from its surroundings that it cannot be confused with other spots in the same image. Locality (also called good localization): the point's exact position is pinned down by its own neighborhood in every direction at once. A straight edge can be distinctive yet still fail locality, because every point along the edge looks the same as its neighbors along the edge -- the aperture problem.
Examples
A window-frame corner is repeatable (the same corner reappears in a second photo), distinctive (it looks unlike the surrounding wall), and local (its position is pinned down in every direction); a point along a straight roofline is distinctive but fails locality, since sliding along the roofline looks the same everywhere.
See also