Symmetry is the preservation of form and configuration across a point, a line, or a plane. In informal terms, symmetry is the ability to take a shape and match it exactly to another shape. The techniques that are used to "take a shape and match it exactly to another" are called transformations and include translations, reflections, and rotations.
An image has Translational Symmetry if it can be divided by straight lines into a sequence of identical figures. Translational symmetry results from moving a figure a certain distance in a certain direction also called translating (moving) by a vector (length and direction).
An image has Reflectional Symmetry if there is at least one line which splits the image in half so that one side is the mirror image of the other. Reflectional symmetry is also called line symmetry or mirror symmetry because there is a line in the figure where a mirror could be placed, and the figure would look the same.
An image has Rotational Symmetry if there is a point in the image that the image can be turned around a certain number of degrees and still look the same.