During a process called Voir Dire which means "to speak the truth" the attorneys will ask potential jurors questions in an effort to empanel a fair and impartial jury.
For instance, if the case being tried involves robbery you may be asked if you or anyone in your family has ever been a victim of robbery. Being excused from a jury in no way reflects on your character or your competence as a juror, so you should not feel offended or embarrassed if your name is removed from the jury list.