The term liberal comes from the aftermath of the French Revolution, where it meant someone who advocated more powerful elected assemblies, in contrast to the alternative of an absolute monarch.
The word has several meanings today. Historically, it was typically used to refer to a person who believed in a free-market economy and a large degree of individual freedom, with a limited social safety net (today known as a "classical liberal"). Presently, in Europe, the word still has a similar meaning (cf. "neo-liberal"). The word is used with this meaning in the names of the Liberal Party of Australia and the Liberal Democratic Party in the U.K.
In the United States, by contrast, "liberal" has come to mean a person who promotes more collectivist economic policies, with varying degrees of belief in individual freedoms. This sort of liberal typically aligns himself with the Democratic Party in the United States, and with the Labour Party in Great Britain.
The latter meaning of the word may have something to do with the idea that "socialism," under that name, is unpalatable to the American people. Norman Thomas, a democratic socialist who ran for president six times on the Socialist Party of America's ticket, said:
The American people will never knowingly adopt socialism. But, under the name of "liberalism," they will adopt every fragment of the socialist program, until one day America will be a socialist nation, without knowing how it happened.
In a more non-political sense, the word can refer to a rejection of traditional views or practices. For example, the American Heritage Dictionary includes this definition of "liberal":
Not limited to or by established, traditional, orthodox, or authoritarian attitudes, views, or dogmas...