The typical Latin honors are "cum laude" ("with honor"), "magna cum laude" ("with great honor"), and "summa cum laude" ("with highest honor"). These are essentially a coarse form of ranking within the graduate class, telling you something about GPA or relative rank.

They are widely but not universally used in the USA, depending on the philosophy of the individual institution: for example, MIT does not use Latin honors or provide any sort of ranking information on its students because it wishes them to be judged individually. As with many other aspects of formal academic organization the US, however, there is no central authority or shared definition, and organizations vary rather wildly in how they actually determine Latin honors, if they even use them. Thus, the only way to know precisely what it really means is to look it up for the individual institution---and even then, they might shift their policies over time.

Bottom line: a Latin honor on a degree means that a student went to an institution that uses Latin honors and they ranked roughly "good", "better", or "best" in their performance there.