We can say that the Civil Rights Movement has many aspects to its legacy. For example, we can say that the fact that we have a president who is half African American is part of the legacy of that movement. Let us look at two general legacies of this movement, one positive and one negative.
On the positive side, the Civil Rights Movement led to greatly improved levels of racial justice in the United States. Before the movement, there was legalized discrimination. Businesses were free to exclude African Americans. The government was free to have laws that required segregation. The fact that these things no longer exist and that there is very little overt racism in the United States any more is a very positive legacy of the movement.
However, we can also argue that the movement had some less positive legacies. For example, the movement brought about the institution of affirmative action programs. These programs have created a great deal of racial animosity without (arguably) serving the purpose they were meant to serve. We can also argue that the racially polarized nature of our political party system was caused by the movement. The movement (and the way it was used by politicians like Richard Nixon) have helped lead to a very negative situation in which practically all African Americans are identified with the Democratic Party. Political parties that are practically segregated by race are not a good thing for our country.