Basic Features of Classical or Civic Republicanism as a Political Philosophy
(1) Human beings are "political animals," suited by nature to organized society or government. The polis is "prior to" the individual.
(2) The state or polis is grounded on the values/virtues/identities of its citizens. Education in these is a central political function.
(3) Freedom is conceived in terms of citizenship, political participation, and non-domination, not primarily in terms of inherent individual rights. Rather, the emphasis is on responsibilities or obligations.
(4) Republican freedom is (hence) compatible with or under some circumstances identical with the rule of law.
(5) Mixed government: republicanism is possibly compatible with constitutional monarchy or more directly democratic forms, but emphasizes a mixture of elements of monarchical, aristocratic, and democratic elements (as in the President, Senate, and House of Representatives).
Some distinctions:
In the Greek political discourse and European-American up until around 1800, "democracy" denotes direct rule by the people. The government instituted by the Constitution tempers democracy with republican elements, including representation and mechanisms for filtering or tempering public will.
Classical liberalism, often associated with such figures as John Locke and John Rawls, emphasizes inherent individual rights and centers the legitimacy of state power in a contract between equal individuals. Republicanism emphasizes the corporate rights of the polis and rests the freedom of citizens on their virtues. Both are elements in the American founding and in what we now think of as the democratic tradition.
Communitarianism is a contemporary political philosophy, associated with such figures as Alasdair MacIntyre and Michael Sandel, that has much in common with republicanism. It treats political questions as being always addressed from within a particularly community's values, language, and conventions. Thus even republican or democratic institutions would only be valid within certain communities. It would refrain from the sorts of universal commitments that republicans embrace, and much more from the universal values professed by liberalism.