Dignified means self-respecting and worthy. If you want to have a dignified memorial service, skip the karaoke machine and instead softly play the favorite music of the person you're remembering.
Something that has dignity is honorable and worthy, so something that is dignified acts in an honorable, worthy way, showing great self-respect and respect for others. If someone handles a terrible public embarrassment gracefully and without breaking down, we might compliment her dignified manner. You might be too dignified to engage in screaming at the wrestling match, or too dignified to beg for a job even in hard times.