When something comes to completion, it's finished. In football, a pass that's been caught is called a completion.
If a wide receiver has a lot of completions, then he had a good day: that means he caught a lot of passes. But if the receiver is out of bounds or drops the ball, then there's no completion. Quarterbacks are judged by their completion rate, too. Off the gridiron, you can use the word completion to talk about anything that's been completed or achieved. Graduation day marks the completion of high school. The completion of a new building or a PhD can take years.