I wholeheartedly disagree with Jeff's statement:
Basically they are saying that you aren't going to do anything good
when you are angry. One can be angry but one's actions will tend
towards sin in these situations.
Unfortunately I don't have the references on me now, but I clearly remember from a particular bible study that being angry is good if you use your anger for good.
Think of say, Erin Brockovich, who used her anger to help a community.
It's also saying that being an angry is not an excuse to sin. If you're angry, you still have to strive to not sin. Hitting your wife because you're angry is not an excuse.
Ephesians 4 can also be about marriage. And in this case, never letting the sun go down on an argument is all about not going to bed angry with your husband/wife.
Going to bed angry means that issues don't get resolved (I should know, I went to bed right after having an argument with my wife last night, and I woke up this morning feeling terrible after a bad nights sleep). Unresolved issues and a failure to communicate are at the core to a failed marriage, and it seems that nothing much in that regards has changed over the last 2000 years.