The Civil Rights Act of 1964 was a major victory for African-Americans because it enforced the advancement of the American ideals of equality and liberty. The most important provisions of the law are its prohibitions on discrimination based on race, sex, religion, language or national origin in the areas of employment and public accommodations (i.e., hotels, restaurants, and so on.)
For more on the Act, see the Wikipedia page here, an article from the CNN web-site commemorating the 40th anniversary of its passage, here, and the US Information Agency's page here.