Achiral molecules are symmetrical and as a result they are identical to their mirror images. One feature of achiral molecules is that they have a mirror plane of symmetry. If a molecule is achiral, you can often imagine dividing the molecule in half, where the right half is the mirror image of the left half. This is not possible for chiral molecules.
Compare 2-propanol to 2-butanol. Do either of these compounds have a chirality center?
In 2-Propanol, carbon #2 is attached to two methyl groups, a hydrogen and an OH group - only three different types of group, so no chirality center is present. You can imagine dividing this molecule into two halves by connecting the red lines - do this and the right side of the molecule is the mirror image of the left side of the molecule. 2-Propanol is said to have a mirror plane where the red lines are in the image - 2-propanol is symmetrical and therefore cannot be chiral. The presence of a mirror plane is one test to determine it the molecule is achiral.
The Molecule on the right DOES have a chirality center - carbon #2 has a Methyl group, Ethyl group, Oxygen and Hydrogen. The four groups attached to the chirality center make this molecule asymmetric. 2-Butanol does not have a mirror plane - there is no way to divide the molecule into two halves that are mirror images of one another.
Another symmetry operation seen in achiral compounds is a center of symmetry ....