Means "latin". The culture and language of ancient Italy. The Roman Empire took over most of Europe and influenced their languages and cultures, so it "latinized" the continent and the new languages are called Romance Languages (with roots in Rome).
After Columbus's discovery of America (the Continent), and the subsequent colonizations of most of the new continent by Spain and Portugal, the latino influence was expanded.
Latino is a person who speaks a romance language (i.e. Italian, Spanish, French, Portuguese) or their cultural heritage comes from any country that speaks any of those languages.
In the US the word latino is misused to name only people from Latin America. The Latin America was a term first created to mean "the part of America ruled by Latino countries, Spain and Portugal" in opposition to the Anglo-Saxon America, ruled by the British (now Eastern United States). In this sense, some parts of the United States are part of the Latin America because they were ruled by Spain at some point (California, Arizona, New Mexico, Texas).
Jorge: We latinos are the best lovers and you whites don't know how to do it.
Giuseppe: You idiot! I'm more Latin than you, I'm from Italy! That's where Latin originated!