By default when Drupal displays a node all taxonomy terms associated with the node are displayed together at the top (or bottom) of the node. While this is really convenient you might want to display the terms in a different way. sort taxonomy links ($terms) by vocabulary ($vid) and Display taxonomy terms broken out by vocabulary are two ways to change a theme so the terms are displayed separately based on their taxonomy. Again, the default is to lump all terms together regardless of the taxonomy the term is in.
Another alternative is to Display only tags (and not other category types) below nodes. That is, rather than displaying all terms from all taxonomies, perhaps you want to display only one or two of the taxonomies.
The Taxonomy system automatically lists node descriptions by the taxonomy terms. For each term in each taxonomy, there is a URL for a page which lists the nodes having that term in that taxonomy. By default the listing of nodes is simply that, a listing of nodes, that looks a whole lot like a blog. Taxonomy Introduction allows you to have a description at the beginning of this list of nodes. For example if you have a taxonomy of U.S. Presidents, and have a term for each of the presidents, the description for each could be a biography and their official portrait.
You might want to display some taxonomy terms as an icon, rather than a word. Replacing certain taxonomy terms with icons shows one way to implement this by modifying your theme. Taxonomy Image does this as a module.