The term “crimes involving moral turpitude” refers to a category of crimes that are said to involve dishonesty, deceit, or a “readiness to do evil.” The list of such crimes ranges from murder to perjury to theft offenses.
Whether a crime is categorized as involving moral turpitude has significance primarily in two areas: court proceedings and immigration. As far as court, when a witness testifies, and that witness has prior criminal convictions, the judge must decide whether to allow the opposing party to impeach the witness with those convictions. Generally speaking, this prior misconduct is admissible only if it's deemed to involve moral turpitude.
As far as immigration, there are several categories of crimes conviction of which triggers “immigration consequences”: deportation, exclusion from admission to the United States, and denial of the chance to naturalize. “Crimes involving moral turpitude” is one category of offenses triggering these consequences.
Of course no one wants to get convicted of any criminal charge. But for many people, conviction for a crime of moral turpitude can be especially devastating.