It's called punitive and/or exemplary damages. To put it simply, a party is punished for their misconduct and so must pay a price for it. Money is the easiest way to pay damages, so money damages are given. The logical receipt of the money is by the people that were harmed. This isn't contract damages. They're not being compensated because they didn't get the benefit of a bargain or because they need restitution. If the bar is found to have violated civil rights then they will be punished for it and that punishment is an example to others to not do the same thing.
I am aware of the US system of punitive damages but I think it is deeply fucked up.
1. It provides a lawsuit lottery that enriches lucky (and/or unscrupulous) few and their lawyers. The amounts are also pretty arbitrary.
2. The purpose of the punitive damages is to punish. The purpose of torts is to compensate for damages. That's why tort law has a low burden of proof (preponderance of evidence). But that burden of proof is not appropriate when you want to go beyond compensating for damages and go into punishment. Thus tort law is being misused to enact penalties.
Why do you think these two women deserve a huge payday just because they were asked to leave a bar? That is not a question about whether the bar did wrong, but solely about the appropriateness of forcing the bar not to pay a fine but to enrich these two individuals and their lawyers. It is also about appropriateness of leveling a punishment (which can me many orders of magnitude above any actual damages) based on "preponderance of evidence" and with the damages amount arbitrarily invented by the jury and not set by any law or administrative decision (where you would have some semblance of proportionality and equal treatment of all violators).