Latin America is a term used to describe nations or territories in the Caribbean, Central America, and South America which were formerly colonial possessions of Spain, France, or Portugal. These three nations speak languages descended from Latin, hence the name. Latin American nations share some strong common cultural roots, such as the dominance of the Catholic Church and, in many Caribbean and Atlantic-facing nations, the influence of enslaved Africans. Many residents of these countries wind up in the United States looking for decent work. This makes conservatives very angry.
Sometimes, the term is used to distinguish the "Latin" countries (current/former Spanish, Portuguese, and French colonies) from the "Anglo" countries (current/former British colonies, with a few Dutch-speaking places thrown in). It is true that the English-speaking Caribbean has its own distinct culture, but a black-and-white division between "Latin" and "Anglo" when discussing the Americas is sometimes a generalization that isn't meaningful, as many Anglophone Caribbean nations share a lot of culture and heritage with their Francophone and Hispanophone neighbors, and there are many countries and territories whose cultures differ greatly despite sharing the same language (i.e., Haiti and the French overseas départements of Martinique and Guadeloupe, or Venezuela and Colombia).
In United States, "Latin America" often means "countries in the Americas that aren't the US or Canada". This definition is used by both liberals and conservatives; for example, when courting Spanish-speakers in the US as a voting bloc (the so-called "Latino vote"). Again, this distinction, while rooted in some truth, is a generalization without much basis in actual history or statistics. While Spanish-speakers do tend to vote Democratic in local and national elections, they are far from homogenous (if you have any doubt, try putting a Dominican in the same room with a Puerto Rican and see how that goes). Furthermore, many US states (Texas, California, Florida, Louisiana) were originally settled as Spanish or French colonies by the same people who settled Latin America. Conservatives in these states tend to de-emphasize this part of history.
Many illegal immigrants to the US are from Latin America. The Republican Party has a reputation for being hostile to immigrants from Latin America thanks to its high concentration of members expressing strong anti-immigration views (see Louie Gohmert or Jan Brewer). This is despite the fact that almost all Americans are descended from immigrants, not to mention the fact that many Latin Americans are phenotypically European, are devoutly Christian, have large families, and don't approve of abortion or birth control.Even though "Latin America" is commonly interpreted as meaning "Spanish-speaking countries," Brazil (with more than 200 million Portuguese speakers) is actually about half as populous as all the Spanish-language countries in the Americas combined (roughly 377 million people).