The word "conviction" has two meanings. The first is an absolute belief in someone of something even though there may be no hard evidence. eg. "I have the conviction that God exists even though I have never seen or heard Him".
The other meaning of this word is legalistic. After a trial in a court of law and after a jury's verdict of guilty, a felon is convicted and his sentence is handed by the judge. An example of "conviction" in this sense is, "The man was being tried for murder and the weight of evidence against him was so strong that his conviction was no surprise to anyone."