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Symmetrical balance (or Symmetry) means that the work of art is well balanced and harmonious. Asymmetrical balance (or Asymmetry) means that the two halves of the work of art are different, however, try to create balance. There are on six types of symmetry as outlined below.

Reflectional Symmetry, the most commonly recognized form of symmetry, occurs when a work of art is the same on one side is as the other, a mirror image of itself, on both sides of a center line. Examples of this include front view portraits, or, sometimes, a character looking at themselves in a mirror.
Rotational Symmetry, another common form of symmetry, occurs when a work of art has the same object rotated around a fixed point, or can be rotated a specific amount around a fixed point, and appear the same as before rotation. Examples of this include the teeth of gears, or the classic designs commonly used on Jack, King, and Queen playing cards.
Translational Symmetry, one of the lesser known forms of symmetry, occurs when a work of art has a duplicate of an object moved in one direction. This is especially true if the object occurs more than once along the exact same dimension. Examples of this are fence posts evenly spaced along a fence line, or the teeth of a saw blade.
Glide Symmetry occurs when a work of art has both rotational and translational symmetry at the same time, that is, an object is mirrored across a center line and moved in one direction. Examples of this are footprints in sand, or zig-zag patterns.
Helical Symmetry, rather uncommon in artwork, occurs when a work of art experiences rotational and translational symmetry in a 3d space. Examples of this would be a perfectly curved slide, or the threads of a screw.
Scale Symmetry, incredibly uncommon in artwork, occurs when a work of art appears the same when scaled up or down. Examples of this would be certain types of fractals such as the Koch Snowflake.

Remember folks, symmetry is art who ever said it isn't art is in the wrong. Good day.