Theoretically speaking, if you are not authorized to be in the United States, you can be arrested immediately, brought before an immigration judge, and deported. Fortunately for millions of illegal immigrants in the US, that is not how the system actually works and that is why they can live fairly comfortably and go on with their lives. For all practical purposes, if you are an undocumented immigrant, stay out of trouble and do not do something that will result in an encounter with law enforcement, the probability of being deported is very very small. That is how the population of illegal immigrants has grown.
In the past, when illegal immigrants were stopped for minor infractions that break American laws, they could be put into deportation proceedings. Obama Administration has some great news for illegal immigrants going forward. If you have never had trouble with the law and have only broken the law for something minor, like driving above the speed limit, you will be treated like a lawful resident. That means that you will pay a ticket but not be arrested or put into deportation proceedings. A host of other petty offenses are going to be treated in the same manner.
Having said that, DO NOT believe even for a second that you are somehow being treated like a legal resident or that you cannot be detained/arrested and deported. Unless it is the very first time that you have gotten into trouble and it is something minor, expect a lot of trouble ahead. Immigration and Customs Enforcement (ICE) is simply saying that it will spend its resources mostly on dangerous immigrants who are either on the run, have committed crimes in the past, or already have a deportation order pending. So while you can breathe a sigh of relief that every time you interact with a cop you will not be considered a suspect and arrested, but the best thing to do if you are here illegally is to never ever break any laws. And that includes, always driving below the speed limit and following all the traffic rules, because while the citizens and legal residents can get away with these violations, you have a lot more at stake.