The fixed pair of observation points in your head (assuming you still have both eyes, and that they are set in your skull) allow you to note an apparent change in the relative position of foreground objects with respect to background objects when you observe them with one eye at a time. When you use both eyes at once your brain does some fancy trigonometry and spits out a figure for "distance" that may or may not be accurate. It is usually good enough to let you successfully snatch food from a friend's plate, but accuracy drops of sharply with distance. Your eyes, it turns out, are too close together (you slope-browed, needle-nosed monkey, you.)
Observing the same distant starfield during the summer and again during the winter allows astronomers to create a stereo pair of observation points that are roughly 300 million kilometers apart (not coincidentally, this is the diameter of Earth's solar orbit). Closer stars will appear to shift in position against the field of background stars. Granted, even with this huge stereo pair the stars don't shift very much. Also, the trigonometry that must be performed cannot be trusted to instinctual mechanisms. This astrometric method is called "annual parallax," and it is most famous for giving us the oft-abused and little-understood term "parsec," which is an abbreviation for "annual parallax of one arcsecond."