Simply put liability in betting is the amount of money you have risked, the maximum that you can lose.
When you make a back bet it's easy to understand, if you bet £10 on Red Rum then your liability is that £10, that's the most that you can lose, your liability.
Where it can get complicated is on the betting exchanges where you can lay a bet or place a bet on a horse or anything else to lose.
Then your stake is not your liability,
With a lay bet your liability is what you have to pay out of you lose.
On an even money bet (2.0) that's straightfoward if you lay £10 at 2.0 your liability is £10.
If you lay £10 at 3.0 which is 2/1 then you are risking £20, the amount you have to pay out, to win £10.
Here's a screenshot from Betfair to clarify.
You can see I am laying Instrumental at 3.0 the backers stake is £10 but my liability is £20, that's what I will lose if Instrumental wins