What is a cladogram and what is not?

What is it about?

Very simply, cladograms are the results of cladistic analyses. They are branching diagrams that group taxa based on synapomorphies alone. Any other tree diagram that is based on a combination of synapomorphies and other information, such as "branch length," is not a cladogram.

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Why is it important?

Words have specific and precise meanings in science, and when their definitions become vague or incorrectly applied, communication is rendered less clear and effective. This is just a case in point of the general lack of appreciation for phylogenetic principles that is blighting the field of systematics nowadays.