That's largely because far fewer white voters came to the polls. Applying exit poll demographic splits to turnout, you can see clearly how many fewer white voters came out on Saturday than eight years ago.
The question -- a particularly important question for Bernie Sanders, if he's to have any chance at beating Clinton -- is why. Was it because moderate white voters moved to the Republican Party since 2008? Because Sanders supporters didn't bother going to vote in an election that he would obviously lose? Because white voters decided to back Donald Trump instead, voting in the Republican primary? The number of white voters fell by 100,000 on the Democratic side since 2008 -- but increased by 280,000 on the Republican side over that same period.
To the first possibility, it's interesting to note that there's been a long slow move away from the Democratic Party by white people. Data from the national General Social Survey has tacked party identification and ideology since 1972, allowing us to see how political attitudes have evolved by race.
If you look at the top light-blue bar on the graph below (data for 1992 was not available), you can see how the number of white people identifying as Democrats has fallen. There was a brief uptick -- in 2008 -- but then the trend continued once again.
Party identification among black people, by contrast, has been more stable, with about 80 percent of blacks identifying as Democratic. (The fluctuations are due to the fact that the sample size from the black population was smaller.) We looked at the history of this last July, but it's not a surprise. Black Americans are much more likely to be Democrats.
We can't tell from this what exactly happened in South Carolina, but if we compare race and party identification to ideology, something interesting emerges. We've noted repeatedly that polling indicates that Democrats are more likely to identify as liberal than they used to, while Republicans have been strongly conservative for some time. Data from Gallup:
That's all Americans. The GSS lets us dive in by race. Here's what that looks like for white Republicans and white Democrats (excluding the "strong" partisans indicated on the graph above -- for reasons that will become obvious shortly).
You can see the slight liberal trend among white Democrats -- and the steady conservative support for white Republicans.
But black Democrats aren't moving in the same direction as white Democrats. Again, there's a smaller sample size here, but you can see that black Democrats are actually more likely to identify as moderate than liberal, compared to 40 years ago.
If we separate out those strong Democrats the GSS identifies, the pattern is even starker. Strong white Democrats are much more liberal than they used to be. Strong black Democrats aren't.
This raises more questions about South Carolina than it answers. (For example: Has South Carolina seen the number of strong white Democrats recede?) But it does appear to help answer the question of why Hillary Clinton is doing so well with black Democrats. Clinton's more moderate politics are more in-line with the black electorate than Sanders's more liberal ones -- which appeal more to strong white Democrats. Nearly two-thirds of strong white Democrats identify as some type of liberal, compared to just over a third of strong black Democrats.
Regardless of why black voters turned out so much more than white ones in South Carolina, it's easy to see from this data why that meant Clinton would win big.