The painting looks like a normal painting, but the portrait will appear to be looking at whoever's looking at it, regardless of how many people there are or where they stand. It's simply the artist's painting technique fooling the eyes with light and shadow.

If they continue to walk down the hall, though, a pair of eyes will emerge from the painting and plop on the ground, rolling after them. This is what the rumors mean by "eyes follow you around," probably.