The fundamental idea is that sometimes people will be arrested and charged with a crime but have an extended period of time before a trial can be held. Most people do not want to wait in jail for that period of time, and the legal system recognizes that it would be unfair to force someone to do so unless there is a reasonable cause to think letting them go free would be a danger to the community or that they would escape entirely. Presuming that a judge considers it reasonable to let them return to the community in the meantime there still needs to be some incentive for them to return for trial.

That is what "bail" is, an amount of money handed over to the court which will be returned in full if the accused shows up for trial at the appointed time. It is supposed to be significant enough that the accused will be reluctant to just leave it behind and avoid the trial completely. This can be in the form of cash or potentially other assets can be pledged such as one's house.

It is possible that this significant sum of money is not something the accused has conveniently on hand. They could instead borrow money in order to pay their bail, and a provider of such a specific kind of loan is known as a "bail bondsman". What they offer is to pay the accused's bail themselves for a set fee, typically 10% of the total bail. When/if the accused shows up to their trial the bondsman gets their money back in full and keeps the 10% fee from the accused.

If the accused doesn't show up for their trial then the bondsman doesn't get their money back. This is a significant risk but there is one way they can mitigate their losses. If the accused is caught and turned over to the courts then they will return the bondsman's money, and in order to make this happen they will offer a "bounty", a reward of money for the capture and return of the accused to the court. The bondsman will need to pay off the bounty but they will get their money back from the court so overall they will lose less money (assuming the bounty is less than the bail + 10%). Those who seek to fulfill the bounty are known as "bounty hunters" and due to the unique legal challenges of a private citizen who's trade is tracking down other people and capturing them against their will, such a trade tends to be strictly licensed so such people are qualified professionals.