Released on your own recognizance means that you are released based on your promise that you will not "go on the run." You sign a paper promising to show up for court. This is not typical of most people in jail; typically it only happens if the person has never been arrested before or has no prior convictions. No bail money is paid. If you've never been in legal trouble and go to jail for a minor crime you'll likely be released on your own recognizance.