Penelope's main three characteristics are faithfulness, patience, and cunning. We can see these in great ways. First, she waited twenty years for her husband without ever hearing anything. Most people would have given up. More than this she has been faithful. This was not easy to do, because there were so many suitors that wanted her hand in marriage. Yet she did not waver, unlike her husband, Odysseus (with Calypso).
Second, she created many ruses to delay and not succumb to the suitors. For example, Penelope stated that she would choose a suitor after she finished making a funeral robe for her father-in-law, Laertes. She would weave it all day long and at night she would undo it. This showed cunning and faithfulness.
Even when she finally met Odysseus, she did not believe it was really him, until she tested him about what he only knew, namely that their bed was built into the house. Again, this showed her wisdom and faithfulness.