The crime of passion defense is basically just a claim that you reacted instinctively when committing a crime, responding to your emotions without thinking. A common example of this type of crime is when someone finds his or her spouse engaging in infidelity and attacks the couple.
This is typically a defense that is used when it's clear that you did commit the crime in question. Most of the time, it's used when someone has been killed.
The reason it's used isn't to prove your own innocence; killing someone in a rage is still illegal, even if it was a cheating spouse. Instead, you're trying to show two things:
1. You wouldn't have acted that way under normal circumstances. You're not a person who is likely to do this again, as you only did it based on a very specific event.
2. You didn't have any time to think about it. When someone is killed, to get first-degree murder charges in Connecticut, it may have to be shown that there was intent to kill and a period of premeditation, where the killing was planned out. If you reacted emotionally, in the moment, you can show that you didn't plan it or meditate on it in advance. This will not get the charges dropped, but it could help you get far lesser charges, such as manslaughter charges, which could massively reduce your sentence.
When facing serious charges, it's crucial that you know all of your defense options. As shown, this is true even when you aren't trying to protest your own innocence, as the case can still be drastically changed with the proper defense.
Source: Legal Dictionary, "Crime of Passion," accessed June 10, 2016