Fredrickson is talking about racism as it exists in the modern Western World. In his view--which is common among modern theorists of race and ethnicity--this kind of racism developed in some forms during the Catholic Inquisitions (when people became uneasy with the idea that a Jew was suddenly just like them by virtue of converting) and really took off as Europe colonized the New World. A driving factor here was labor; it was suddenly very important to justify why some people could be enslaved or, in the case of the native populations, exterminated/supplanted. And again, there was a religious component; although a Christian might be able to justify enslaving an African because he was a pagan, the Christian needed a new reason after many of his slaves had converted to Christianity.

Eventually the way of thinking that developed from all of these factors became so entrenched that it got into many other parts of life, and sort of broke free from its origins. As Anibal Quijano puts it, "The racial axis has a colonial origin and character, but it has proven to be more durable and stable than the colonialism in whose matrix it was established" (533).

Quijano and Fredrickson think it's important to say that racism may seem like human nature today, but, at least as we experience it in the world, it has a historical origin, even if it sometimes feels like the natural state of affairs. That's not to say that things that sort of look like modern racism have never existed anywhere else in the world (see other replies about barbarians, etc.), but when we talk about it today, we should understand that it's something humans have invented over time (and, hopefully, can therefore dismantle).

Sources:
Here's the Quijano paper I'm citing.
For Fredrickson, I'm mainly referring to the first few chapters of Racism, A Short History, linked here.

OP, the link isn't working.

As a follow up: I understand that race the way we conceive of it is a relatively recent phenomenon, how were differences in skin color perceived by different cultures throughout history? What sort of regional variation was there?

"clear and unequivocal" are weasel words. They can mean whatever he wants. If you provide evidence, he can say it's not clear and unequivocal.

I'd be interested to know if anyone who has more knowledge of ancient Greek history could discuss the relationship between Spartans and Helots. From my reading they seem to be different ethnicities, and it fits in with Fredrickson's definition of racism, but I only have a basic understanding of Sparta.

One thing I noticed from reading a couple of different post-17th century first-hand European accounts of foreign nations is the preoccupation with race and racial superiority. Pretty much everything involved in contact with Asians or Africans or Natives was steeped in racial discourse. Note the separation between ethnicity and race in this case. I read lots of mentions of the camaraderie between Europeans based on their race in face of other aggression; in fact that's where the "blood is thicker than water" saying comes from, it's not about family relations but an American deciding to defend British ships from Chinese attacks due to the "white blood", so to speak.

So I suppose this obsession with race is really something that we don't often see in writings before this period. For example we never see Chinese entities express camaraderie with Filipinnos or Japanese just because they're all Asian. The key is that this sort of racism is separate from simply ethnic concerns; people holding these beliefs know the difference between ethnicity and race, and hold prejudices based on each. It does seem to me that the post-middle age views on race were pretty different from earlier views, even if you can't really say that earlier cultures weren't "racist".