Central America isn't a continent. It's a political designation that simply exists for Americans to "other" neighbors. (When not meddling in their politics.)
There are 7 continents: Asia, Africa, North America, South America, Antarctica, Europe, and Australia. Central America and the Caribbean are regions of North America.
From Wikipedia's article on Central America:
"Central America consists of seven countries: Belize, Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua and Panama."