plane of symmetry
Hold a butterfly upside down in your mind and slide an imaginary sheet of glass straight down its middle. The left wing is the mirror image of the right wing — the glass divides the butterfly into two reflected halves. That imaginary dividing mirror is a plane of symmetry, and finding (or failing to find) one inside a molecule is the surest way to decide whether the molecule is chiral.
A plane of symmetry is an imaginary flat plane that slices an object into two halves, each the exact mirror reflection of the other. A molecule that possesses such an internal plane is achiral: the plane itself guarantees that the molecule is superimposable on its mirror image, because the two halves already are mirror images. To search for one, look for a way to bisect the molecule so that every atom on one side has a matching atom directly across the plane. If you can do it, the molecule is achiral; if no such plane (nor any other improper symmetry element) exists, the molecule is chiral.
This single idea is the workhorse test of stereochemistry. It explains why a molecule with two stereocenters can still be optically inactive — the famous meso compounds owe their achirality precisely to an internal mirror plane that cancels one half's handedness against the other. When in doubt about whether a complicated molecule is chiral, drawing the most symmetric conformation and hunting for a plane of symmetry is almost always faster and more reliable than counting stereocenters.
meso-2,3-dibromobutane, CH3-CHBr-CHBr-CH3 with one Br up and one down, has a mirror plane running between the two central carbons: the top half reflects exactly onto the bottom half. That plane makes it achiral despite having two stereocenters.
An internal mirror plane forces a molecule to be achiral, even with stereocenters present.
A plane of symmetry is sufficient to prove a molecule achiral, but its absence is not quite the whole story: chirality strictly requires the absence of any improper rotation axis (which includes the mirror plane and the center of inversion as special cases). For nearly all molecules you meet, however, the plane test settles it.