A more thorough explanation:

A peremptory challenge is a special type of challenge that each party in a trial is allowed to use to exclude a potential juror without giving any reason or explanation. However, if the opposing party believes that the peremptory challenge was used to discriminate against a juror based on their race, ethnicity, or sex, they can present a prima facie argument to challenge the peremptory challenge. This is known as a Batson challenge.

In a criminal trial, the defense attorney may use a peremptory challenge to exclude a potential juror who they believe may be biased against their client. For example, if the potential juror has a family member who was a victim of a similar crime, the defense attorney may use a peremptory challenge to exclude them from the jury. However, if the prosecution believes that the peremptory challenge was used to exclude the potential juror based on their race, they can present a Batson challenge to challenge the peremptory challenge.

Another example could be in a civil trial, where the plaintiff's attorney may use a peremptory challenge to exclude a potential juror who they believe may be sympathetic to the defendant. For example, if the potential juror is a business owner and the defendant is a corporation, the plaintiff's attorney may use a peremptory challenge to exclude them from the jury. However, if the defense believes that the peremptory challenge was used to exclude the potential juror based on their gender, they can present a Batson challenge to challenge the peremptory challenge.

These examples illustrate how peremptory challenges can be used by both parties in a trial to exclude potential jurors without giving any reason or explanation. However, if the opposing party believes that the peremptory challenge was used to discriminate against a juror based on their race, ethnicity, or sex, they can present a Batson challenge to challenge the peremptory challenge.