Heroism, simply, means acting like a hero. A hero is someone who possesses great bravery, courage, and valor. So heroism means acting in a way that shows those qualities.
Ex: The Queen herself was on hand to present Captain Moore with his award. In a short speech, she praised Captain Moore's deeds, citing his great heroism.
Ex: The heroism displayed by the entire group of Boy Scouts when their Scoutmaster slid down the cliff and broke his ankle was astounding. They all acted more like men than boys that day, risking their own lives to rescue him.
If you want to talk about someone whose acts of heroism go without being noticed, you would call that person an unsung hero. When popular opinion about someone changes from apathy to great admiration, you might say that he or she has gone from zero to hero.
Ex: There were many unsung heroes on the day of the earthquake, including all of the teachers at Cedar Ridge High School, who calmly led their students out of the building just before it collapsed. None were hurt.
Cowardice is a lack of courage and bravery. Someone characterized by cowardice does not stand up for what is right for himself or others.
Ex: When the Titanic was sinking, the rule was that women and children were the first to board the lifeboats. When a man was discovered wearing a dress and trying to sneak aboard a boat, it was seen as the ultimate act of cowardice.
Ex: In much the same way that bravery leads to greatness and fame, cowardice leads to shame and infamy.
Cowardice refers to a type of behavior, whereas coward refers to the person who fails to act with bravery when called upon to do so.
Ex: Many people think that bullies are usually cowards underneath a false exterior. The minute someone turns the tables on them, they run away in fear.
Ex: One thing you can be sure of is that you can't be a coward if you're a police officer or firefighter. Those jobs are just too dangerous to be done by anyone lacking courage.