If we have the group (dihedral group under operation of composition), the only elements in the group are the rotation elements and the reflection elements about the axes.
Some interesting characteristics are:
1) if you compose one reflection with another reflection, you get a rotation
2) if you compose one rotation with another rotation, you get a rotation.
3) if you compose a rotation with a reflection (or vice versa), you get a reflection.
4) has a commutative subgroup (rotations). I.e. in (the symmetry group of the equilateral triangle), the rotation subgroup is . It is apparent that
5) has an order of (order refers to the number of elements the group has [i.e. has 6 elements ]).
There are probably more things, but that's all I can think of at the moment.
Does this shed enough light on what Dihedral Groups are? You can always find more information on the web. You can find more info here.