The term African-American is commonly used to refer to the racial category "black". It was invented in an effort to avoid negative connotations or a perceived sense of being coloquial when using the term black, by putting blacks in the same normative position as other "hyphenated Americans". Black, in turn, was preceded by Negroid and Negro, both of which derive from non-English words for "black" and acquired a negative connotation largely through their similarity to the pejorative term "Nigger", which has never been polite.
The term has not worked perfectly. It has not replaced black in common or even all formal communication. It has had difficulties in part because it conveys false precision. African-American, at face value, ought to include white individuals who are born in Africa but live in the United States (such as Teresa Heiz Kerry and many South African whites), but such a useage is often considered deceptive, because the term is really a substitute word for "black". Similarly, few people in the United States would consider a person with South Asian ancestry whose family had lived in Zanzibar for generations to be African-American. The term African-American also creates confusion by failing to make a distinction between black individuals who have lived in the United States for decades, and recent immigrants from countries like Nigeria and Ethiopia. Likewise, it is not clear to what extent a recent immigrant from North Africa, who is likely olive or light skinned and more Mediterranian -semetic in features is an "African-American", even though this is not necessarily viewed as quite so deceptive as an ex-patriot white American's claim to be African-American.
There is also a lurking issue concerning "who is black"? The census now permits people to mark more than one race. For example, a person with a white mother and a black father could check both black and white. But, race is primarily a social construct, and while Latin American and early North American social systems made a distinction between mulatto (part-white and part-black), the social system used in the modern United States does not, and most "African-Americans" in the United States would properly be classified as "mulatto" if it did. Instead, the colloquial standard used by average people in the United States is the "one drop rule" (i.e. that anyone with some African-American ancestry is considered African-American). While distinctions are made between lighter and darker skinned blacks in the United States, the distinction is not recognized by significant numbers of people of any race as a "difference in kind". Part of the political motivation behind seeking a "more than one race" category for census purposes was to overcome the "one drop rule".