What is a parallax error?
Parallax error (in astronomy) is the error in measuring distances to nearby stars.
The nearby star that is being observed changes position with respect to the background stars when calculating distances.
Think of a a block of wood being measured with a ruler.
The ruler isn't completely flat, it has three dimensions (length x width x height). That height is typically just a couple millimeters, but that accounts for parallax error when viewing the ruler from different angles. The same goes for stellar parallax error.
Take a look at these pictures for a better visual on what is happening.
Angled from the right:
Angled from the left:
So, as you can see:
Angled from the right looks like an over-estimation; conversely, from the left is an under-estimation. Whereas, directly above is the exact measurement.
As we move our viewing angle, the apparent measurement changes accordingly. This is why stellar parallax can only be used for nearby stars since our instruments are only sensitive enough to measure these . . . as of yet.