You know the lawyers who try to make the jury believe the guy on trial for stealing the bananas actually stole the bananas? That team of lawyers is known as the prosecution.
The entire process of trying to convict someone of a crime is known as the prosecution, and if convicted, you may face prosecution. Any words with the root prosecute are connected to trying to prove someone’s guilt. You might often hear about "the prosecution's case" — that's their evidence. Or you might hear about a "prosecution witness" — someone who is supposed to tell jury members something that will convince them of the defendant's guilt.