In this quote, he is specifically referring to people like Bob Ewell, who knew that if he accused a black man of rape, that man would be convicted, just because of racism and discrimination that exists. If he were to accuse a white man of rape, the odds would be more "equal" than they were in Tom's case. Bob knew that Tom being black would gurantee Tom's verdict of guilt; he took advantage of a man's race to do serious evil.
Also, Atticus, in this quote, is teaching his children a very important moral lesson. In the quote, he is saying that because black people in their society get such a rotten deal, because they are put down, spit upon, considered to be the lowest of the low, ostracized from society, not respected, and given the hardest, dirtiest work that there is, that they have a rough time in life. And because they have the hardest time in life, to treat them poorly is to take advantage of the weakest among all people. It is like taking food from a starving child; the black people don't get any respect or any opportunities in their lives, and so to cheat them is to treat them like scum, and to be just one more white person that reinforces discrimination. White people didn't have to struggle the same way that black people did. Black people, just because they were black, were constantly being cheated by white people; Atticus does not want to be one more white person taking advantage of a black person. He doesn't want the cycle of racism and discrimination to continue in himself and his children. He says you should treat everyone with respect, but moreso those people that deserve a fair chance because they never get one anywhere else.
I hope those thoughts help to explain the quote a bit. Good luck!
In "To Kill a Mockingbird," Atticus states that "cheatin' a colored man is ten times worse than cheatin' a white man.. it's the worse thing you can do"
In this quote Lee is cutting to the heart of the theme in this novel. During this era in American History the African-American was basically less educated than the white people in many communities. That is not to say there were no educated Black people, but the majority were innocent and uneducated. Lee, through Atticus is saying that because the Black man was innocent, and less savy than the white man, it was a terrible thing to cheat him. To cheat someone who is so innocent and unsuspecting is the same thing as killing a Mockingbird. The person who would cheat someone who is trusting, innocent and unsuspecting is worse than cheating someone who should know better.
"The most obvious instance is the case of Tom Robinson: the jury's willingness to believe what Atticus calls "the evil assumption . . . that all Negroes are basically immoral beings" leads them to convict an innocent man. Boo Radley, unknown by a community who has not seen or heard from him in fifteen years, is similarly presumed to be a monster by the court of public opinion."
When you cheat someone who is innocent, like the system cheated Tom, it takes some of that innocence away from the cheated person. This is not right and does not fit into Atticus's value system. Atticus is trying to teach his children to be fair to everyone, especially to the weaker people in their society.