Chemists classify molecules according to their symmetry. The collection of symmetry elements present in a molecule forms a “group”, typically called a point group. Why is it called a “point group”? Because all the symmetry elements (points, lines, and planes) will intersect at a single point.
So let's look at a specific example, say water. What symmetry elements does water possess? Identity, E; two reflection planes, σxz and σyz; and one 2-fold rotation axis, C2. In the common notation (aka Schoenflies notation), this is known as the C2v point group.
Another molecule that also belongs to the C2v point group is cyclohexane in the boat conformation. Look at the two figures below and see that they do contain the identical set of symmetry elements, even though their overall shapes are quite different.
Determining Point Groups
So how does one determine the point group of a molecule? One possible approach is simply to find all the symmetry elements and then look at a set of tables (something called character tables will work) until you find a matching set. While this would not be hard for something as simple as the example above, molecules like methane that contain 24 symmetry elements would be more tedious!
So chemists have developed various flowcharts that make the process as simple as answering a serious of yes/no questions. If you would like some practice in this process, you can go to the Symmetry Challenge page of this web site and find out how it works.