Waiting until the last minute to finish something can mean:
You'd procrastinating or would like to avoid whatever the activity represents
You're afraid you'll end up having to rush something at
The last minute
You're feeling passive-aggression towards an authority figure, perhaps the one who assigned you the task
Something coming through at the last minute (such as finding a solution or being saved) can mean:
You're waiting for something in real life that seems to be taking a long time
You're wanting or waiting for some help or support right now
You desire more excitement in your life