Symmetry is when elements are arranged in the same way on both sides of an axis. Perfect symmetry is when elements are mirrored over the axis and exactly the same on both sides.
Symmetry adds balance to a design. It is when elements are the same on both sides of an axis. An example is 5 houses on each side of a street. It feels balanced.
Designs are asymmetrical if the arrangment of elements are different on both sides of an axis. An example is the Pinterest feed. The size of elements in the feed vary.
Example