Something symmetrical has matching halves — you could fold it down the middle and the two sides would lie exactly on top of each other. A butterfly. A human face, roughly. The letter A. A well-planned garden with the same three trees on each side of the path.

The everyday meaning is that mirror one. Maths adds more kinds: rotational symmetry, where a shape looks the same after you turn it part of the way round (a five-pointed star, a snowflake); point symmetry; symmetry across more than one line. So a mathematician calling something symmetrical may not mean left-and-right at all. And the word travels well beyond shapes: a symmetrical argument treats both sides by the same rule, a symmetrical trade agreement gives each country the same terms, symmetrical warfare means two sides fighting with comparable weapons — which is why the news says asymmetrical warfare for the other case.

The opposite words matter here. Asymmetrical means the halves do not match. Unsymmetrical exists but sounds clumsy; native speakers reach for asymmetrical. In fashion and design, asymmetrical is often a compliment — an asymmetrical haircut is deliberate.

Though actually — be careful with 'perfectly symmetrical', because almost nothing real is. Faces are close but not equal, and studies keep finding that people rate slightly imperfect faces as more attractive, not less. Buildings that look symmetrical are usually adjusted by hand so they will look right rather than measure right. So in careful writing you will see hedges: roughly symmetrical, near-symmetrical, symmetrical at first glance. The word describes an ideal that objects approach.

One more thing worth knowing: symmetrical and symmetric mean the same thing, and both are correct. Symmetric is preferred in mathematics and physics (a symmetric matrix), symmetrical in ordinary description. Do not spend energy choosing; do not use both in one paragraph.