A concurrent sentence it one that runs at the same time as another. Consecutive sentences run one after another.
For example, imagine an accused person is charged with third-degree grand theft and possession of cocaine in the same information. Both are third-degree felonies punishable by a maximum of 5 years in prison each. The judge sentences this defendant to two years of probation to run concurrent on each count.
That means that the accused will serve a total of two years of probation for both charges. The terms of probation will run at the same time.
Now pretend that somebody with serious criminal priors is charged with aggravated battery and possession of marijuana in the same information. Aggravated battery is a second-degree felony punishable by a maximum of 15 years in prison, while possession of marijuana is a first-degree misdemeanor punishable by a maximum of 364 days in jail.
If sentenced consecutively, a judge could sentence this defendant to 15 years on the aggravated battery followed by 364 days on the possession of marijuana count. Since the sentences run one after the other, this is a consecutive sentence. That means that while serving the aggravated battery sentence, this defendant will not have begun to serve his possession of marijuana sentence until the aggravated battery sentence expired.
Most sentences are concurrent sentences. This includes sentences imposed by judges and those agreed to by the State and defense through plea negotiations. Unless there are extenuating circumstances, the charges are particularly heinous, or the defendant has a substantial criminal record, chances are that the Court will not impose consecutive sentences.