Indignation is a form of anger. It's an angry reaction to something that is unfair, mean, or unjust. It's also called "righteous anger."
What does indignation mean?
Have you ever been yelled at for something you didn't do? What did you feel? You got angry, right? How did you respond? It was with indignation!
Or imagine this: After a lot of research, you developed a brilliant idea for the science fair and told a bunch of people about it. Unfortunately, someone copied your idea — and won first place! How do you feel? Indignant!
Indignation is the noun (specifically, an abstract noun).
Indignant is the adjective.
Indignantly is the adverb.