This is the news headline I see on Fox News.
Tom Fitton: Kavanaugh-Ford hearing didn't advance the ball
What is the original meaning of "advance the ball" in sports? And what is its analogic meaning in this Kavanaugh-Ford hearing news?
In many ball sports, the aim of the game is to get the ball past your opponents and into a "goal" of some kind. For example in (American) football, the aim is to carry the ball forward into the opponents "end zone". In each play, the team attempts to advance the ball as far as possible.
Metaphorically then, "advance the ball" means "make progress towards some ultimate goal", in the specific example, it means that the hearing didn't change the opinions of people, neither for or against Kavanaugh.
In American football, the goal is to advance down the field with the ball to score a touchdown. However, on some plays you can't advance and get stopped by the defense. Listening to the rest of Fitton's sentence, the analogy he's making is that the Democrats would "score a touchdown" by getting Kavanaugh's nomination to fail, but the hearing did nothing to bolster support for that, so they're stuck in place.
Advance the ball here means: determine who is telling the truth: Kavanaugh or Ford. One of them is lying.
Truth being the goal.
The aim of the hearing with them was to see if one could find out who is telling the truth: Him or her.
In any kind of football, one seeks to advance the ball. Get ahead of the other team so one can score.