"Thru" is how many holes a player has finished in the current round. Thru 12 means twelve down, six to go. It tells you how much of the day is still ahead of them, which is what makes a lead feel safe or shaky.
A few symbols you'll see next to it:
F — finished. All 18 holes done for the day.
E — even par. Not a thru number; it's a score. The player is exactly on the course's par.
* — a star after the number, like Thru 9*, means the player started on the back nine (the 10th hole) instead of the 1st. Tournaments do this to get everyone round in daylight. They've still played nine holes; they just played them in a different order.
— — nothing yet. The player hasn't started today's round.
One thing to watch: a player at -6 thru 10 and a player at -6 thru 17 are tied now, but the first one has eight more holes to move. That's why AllTee shows thru next to every live score, never a score on its own.