So for instance, MOM has vertical symmetry because it can be rotated on it's vertical axis without changing the word (imagine drawing a line down the middle of the O, and flipping the word on that line). But if you rotated MOM horizontally, you would get WOW -- therefore, MOM does not have horizontal symmetry.
Some words that do have horizontal symmetry include BED and COOK.
Check out Word Play for some examples of pretty long words with vertical or horizontal symmetry, but before you do, can you guess the following:
1. A word that has 180-degree rotational symmetry (if you grabbed the bottom right corner of the word, and spun the word halfway around so that this corner now became the top left, and you ended up with the same word)?
2. A word that has horizontal symmetry when in capital letters, but vertical symmetry when in small letters?
You'll find the answers here.