Heritage, pride, history... All these things factor in. Some people use it for racism, too, yes, but not everyone who respects this flag does.
What it means to me is something I can agree with. Something the Civil War was fought over. No, not slavery. That wasn't the issue the Civil War was fought over, despite what you might have been lead to believe. That was simply the sub-issue. The real issue the Civil War was fought over was the rights of the state versus the rights of the federal government. The Confederate states rebelled because the laws being handed down from Washington contradicted their own state laws, and they believed that the state laws had precedence and should not be over-ruled. True, the laws at stake were laws regarding slavery, but that was not the main reason the people were fighting. The Confederates were in essence re-enacting what happened in the Revolutionary War. Laws were being handed down from "on high" without regard to what any of the people directly involved thought. No opinions were gathered. No representatives had their say. It was just "make this a law" and that was it. So, the Confederates rebelled against the Northerners the same way the 13 colonies rebelled against England. If they had been better organized, they might have succeeded in their rebellion and founded a new nation. So, just because I agree with the Northerners on this issue, in that slavery of any kind is wrong, I do not agree with how the issue was dealt with by the Northerners. What should have been done was for the government to hear the issues at stake and opinions of those directly affected, and then make a decision. People who feel that their opinions have been heard are less likely to get upset, even if they don't agree with your final decision.
Now, let's take a modern issue that's about as polarizing now as slavery was back in those days: gay marriage. I am personally against any laws regarding gay marriage. (Before I get flamed, see my note at the bottom.) However, I believe that each state should get to decide what they want to do about the issue rather than having a federal law over the whole country. No matter what your views on marriage, be it gay, straight, polygamous, group, or whatever, it will always be a local matter, rather than a national one. Your marriage really only concerns those in the general vicinity. Marriages in California will likely have no effect on me in Maryland, and vice versa. Therefore, the laws should be on the more local level as well, as the people in California are different from the people in Maryland, and, therefore, should be treated differently. There are currently several states that permit gay marriages, as well as several states that ban them. I am absolutely fine with both of those, because they were added to state Constitutions by votes of the people, and the people chose what they wanted. The people should have the say, and not the "almighty" government who sits above us trying to force everyone into one mold. We all simply won't fit into it.
So, therefore, to me, the Confederate flag symbolizes the fight for states' rights and the fight against "big government."
Note: Alright, I need to explain my position before anyone pigeon-holes me. My opinion is non-standard on either end of the debate. What I believe in is that the government, if it truly believes in "separation of church and state" (which is NOT in the Constitution, by the way) should have no business in marriages of any kind. The term "marriage" is a religious term at its core. If the government wants to be truly neutral on religious issues, I have a plan on how to fix this one. First, you simply abolish all current marriages. Then, you form "civil unions" (or whatever the PC term currently is). Then, you simply define what a "civil union" is, be it straight, gay, group, or whatever. That will be up to the people. (That is the key. The people decide on it.) Then, finally, you grandfather clause all previous marriages into the new "civil union" system. This way, even if the government allows same-sex civil unions, those with moral or religious issues will not be bothered by the term "marriage" being applied to a same-sex couple. They can simply rationalize it in their heads that these two are not really "married" in a way that is meaningful to them.