I'm first going to ignore the more difficult problem: culture. Let's first concentrate on the slightly simpler problem that we know (or at least are fairly sure of) the answer to: race. Specifically, the biological definition of race: haplotypes and haplogroups.
First let me give some simplified definitions of these words in case you are not familiar with them (though I recommend googling them if you find this topic interesting):
A haplotype is a set of genetic differences that are usually inherited together. For example, the genes that give someone blond hair will usually be inherited together with genes that give them pale skin. It should be noted that there will always be exceptions in a population but there will also always be a general pattern.
A haplogroup is a population of individuals that share common or similar haplotypes.
When talking about humans, we link haplogroups to races. It should be noted that they are not strictly equivalent. Each traditional "race" is usually made up of several haplogroups. For example, this is the haplogroup distribution of the Turkish people:
So each race is made up of many haplogroups. You can think of haplogroups as "genetic race" or ancestor race. Each race we recognise today is made up of many ancestor races instead of just one.
When talking about animals, we link haplogroups to breeds. Just like humans, each breed is made up of several haplogroups. Also just like human races, a breed is not a species. Different breeds of a species are still a member of that species.
Now that we have established an equivalence between breeds and races, let's talk about the simpler case: animal breeds.
Some species of animals come in a wide variety of breeds. The most obvious example is probably dogs. Some may not realise it but all dogs are of the same species: Canis lupus familiaris.
Some species of animals on the other hand come in only a single breed. One example is the mallard. Excluding crossbreeding with other species, there is only one breed of mallards.
Most animals are somewhere in between. Most species come in three or four breeds scattered geographically.
So, what determines the number of breeds a species has? For dogs it's obvious: we created them deliberately (basically inbreeding). For mallards (and most migratory birds) the reason that there's only one breed is that the species is highly mobile (they're migratory after all) and all members of the species have the same opportunity to mate with any other member. This results in a homogenous species. For most animals the number of breeds correlates strongly with the number of herds/pride/gang/groups there are and how isolated they are from each other. The main reason breeds exist is because not everyone in the mallard species can mate freely with anyone else. Matings mostly occur in the same neighbourhood and very rarely between two populations. So basically inbreeding.
Now, the exact same reason determines how races developed in humans. Since humans are scattered everywhere on the surface of the planet and travel is expensive it is more likely for people who live in the same area to start a family and very unlikely for people who live far apart to do so.
Having stated that, of course it's obvious! I didn't even need to explain about genetics and all the examples with animals. But it's important to correctly identify the real factors involved rather than just stating the obvious.
So the factor that determines how diverse or monolithic a species is is simply isolation. Make travel cheap and easy and you end up with a species that only have a single race. Make travel expensive or restrictive and you end up with diverse races. Make society accepting and inclusive and you eventually end up with a single race. Make society racist or biased (no matter how subtle) and you end up with diverse races.
Culture works sort of the same way. Culture is our shared experience of what a society is. Thus when we isolate a group of people (or they isolate themselves) they tend to develop their own in-jokes, their own sense of right and wrong, their own sense of style etc. Culture is also different in that it can spread through the media.