To misspeak is to say something the wrong way. You can misspeak by pronouncing someone's name incorrectly, or misspeak by saying something that accidentally offends them.
Sometimes when politicians are called out on controversial things they say, they claim to misspeak. Saying that you misspeak implies that a mere slip of the tongue kept you from saying the right thing, and allows you to set the record straight. In the fourteenth century, to misspeak was both "to say amiss," and also "to speak insultingly," from the Old English missprecan, "to grumble."