There are several definitions of Latin America, none of them perfect or necessarily logically consistent:
In most common contemporary usage, Latin America refers only to those territories in the Americas where Spanish or Portuguese prevail: Mexico, most of Central and South America, plus Cuba, the Dominican Republic and Puerto Rico in the Caribbean. Strictly speaking, this is called Ibero-America (a term widely used in Spain -as well as Hispano America-, but not in Latin America).
Strictly and technically speaking, Latin America designates all those countries and territories in the Americas where Romance languages (i.e. languages derived from Latin, and hence the name of Latin America) are spoken: Spanish, Portuguese, and their creoles. Indeed, this was the original intent when the term was coined by the French. This would then include former French colonies such as Quebec in Canada, Haiti, Martinique and Guadeloupe in the Caribbean, and French Guiana in South America.
The former Dutch colonies Suriname, the Netherlands Antilles, and Aruba are not usually considered part of Latin America, even though in the latter two, the predominantly Iberian-influenced language Papiamento is spoken by the majority of the population.
Sometimes, particularly in the United States, the term Latin America is used to refer to all of the Americas south of the U.S., including countries such as Belize, Jamaica, Barbados, Trinidad and Tobago, Guyana, and Suriname where non-Romance languages prevail.
Indeed, in historical terms, Latin America could be defined as all those parts of the Americas that were once part of the Spanish or Portuguese (and arguably also French) Empires. Hence much of the US Southwest plus Florida (and also French Louisiana) would be covered by this definition.
Finally, it's worth noting that the distinction between Latin and Anglo America, and more generally the stress on European heritage, passes over the fact that there are many places in the Americas (e.g. highland Peru or Guatemala) where non-European cultures and languages are still important, as well as the influence of African cultures in other areas (e.g. the Caribbean, including parts of Colombia and Venezuela, and coastal Brazil).