Standings are gained and lost as campaigns, missions and other content that affects standings takes place. For example, capsuleers killed in campaigns will have a low opinion of you which has a knock effect with their corporation and alliance. The agent or agency that you killed them for on a camapign will have an increasing opininion of you. Standings affect your rewards from agents and agencies.

TOWARDS: usually due to others running campaigns/missions/other for crisis management

AGAINST: usually due to crisis management running campaigns/missions/other for agents/agenies or carrying out hostile actions against others.