A jury convicts a defendant of two charges. The judge sentences her to three years in prison for Count 1 and two years in prison for Count 2, with the sentences to run consecutively. What's the total prison sentence?
The total prison sentence is five years. (But note that defendants typically don't spend all of their jail or prison sentences behind bars, whether because of credits one earns while in custody, parole, or some other criminal-justice concept.)
When sentences run consecutively, the defendant serves them back to back. When they run concurrently, the defendant serves them at the same time. So, if the judge in the above example were to order that the sentences run concurrently, the defendant's sentence would be three years—she would serve the two-year sentence simultaneously with the three-year sentence.
For more detail on these concepts and the surrounding law, see Concurrent and Consecutive Sentences, and Double Punishment.