Mechanically, demihumans offer a few things.
Firstly, they can multiclass in the old-school (pre-3E) style, in which you get all the abilities (or at least the majority of them) for two or more classes. Humans can multiclass in 3E style where they split their total abilities adding up to 100% of a single class; the demihuman ability to spend more than 4 points total allows them to get 100% of more than one class.
Secondly, they offer the ability to trade maximum power for early power. They can spend more than 4 points total, but doing so reduces their maximum level, pretty significantly if you want to end up with a lot of points. An elven spellsword begins the game with a lot more power than either a human fighter or a human wizard, but their level cap of 10 means that they will never reach the heights of power that either one will gain in their bailiwick. (And arguably this will make them weaker at maximum level than either of the human classes, an argument that is relatively easy to make when comparing them to a 14th level wizard and harder to make when comparing to a 14th level fighter).
Related to the second point, their ability to spend a lot of points gives them the ability to create classes with very high XP costs. A class with a very high XP cost starts off very strong at 0 XP, but gains in power very slowly compared to other classes. Consider again the elven spellsword (which wins the prize for ‘highest base XP cost’ in ACKS, although the Thrassian gladiator’s continuing to double after 8th allows them to win the prize for ‘highest XP cost to max level’); an elven spellsword at 5th level has just learned Fireball (or is about to research it) and is very excited about it. The party wizard learned Fireball 12,000 XP ago and is almost 6th level; he’s been casting it for ages.
In terms of setting, the things offered by demihumans will of course vary based on the specific setting. The primary trick they enable is multiculturalism. Having different demihuman races stand in for different cultures, instead of having different subspecies of humans do it, makes it easier to have fantasy racism without it also being real racism. It also lets us imagine what sort of cultures an alien race (demihumans are basically aliens, in the sense of intelligent beings who are not human and might have different ways of thinking or cultural mores based on the differences between them and humans) might have.
Dwarves, for example, who are all hardy people and skilled craftsman, would be a lot more likely to start the Industrial Revolution earlier than humans. They don’t need the level of safety precautions that humans do, because dwarves can breathe asbestos and coal smoke all day and be fine, which means they would be more likely to do it earlier as they could survive it at a lower technology level.
Elves are more likely to end up with a geriocratic society, because elven bodies do not decay as they get older. ACKS elves remain hale and healthy their entire life (barring sickness or injuries), while continuing to gain in knowledge and experience. This means that they’re more likely to end up with a society where the older you are, the more status you have than humans are.
And so on. The actual physical differences between the demihumans can be used as springobards for figuring out what kind of cultural differences they’d have from humanity.