A heinous crime is very evil or wicked. Of course, some people only use the term as an exaggeration, claiming that their parents' requirement that they write thank you notes after their birthdays is a heinous form of torture.
Heinous descends from Middle English, from Old French haineus, from haine "hatred," from hair "to hate." So when you want to use the word heinous in all seriousness, think of acts that are considered hateful (or outrageous, and shocking). Think: treason, torture, the clubbing of baby seals. Heinous is pronounced HĀ-nəs.