Mulatto is a historical term for people who are born of one white parent and one black parent, as well as mixed-race people in general. However, the term mulatto is now considered to be derogatory and offensive.
Mulatto arguably has the ugliest roots of antiquated ethnic terms. The term originated from the Spanish word mulato, which came from the word mula, or mule, the offspring of a horse and a donkey; an offensive and outdated term.
Due to the word’s troublesome origins, it's best to refrain from using it in any situation.
The word should never be used in casual conversation to describe a biracial person. Terms such as biracial, multiracial, multi-ethnic or mixed are usually non-offensive, with mixed being the most colloquial.
Sometimes people use half-black or half-white to describe mixed-race people, but some biracial people believe these terms suggest that their heritage can be literally split down the middle like a pie chart, while they view their ancestry as completely fused. It's safer to ask people what they wish to be called or listen to what they call themselves.