If you take someone to a restaurant and tell him that you are going ‘to foot the bill’, what you mean is that you are going to pay the bill.
Example: “I’m willing to come along if you promise to foot the bill”.
The ‘foot’ in the expression has nothing to do with our feet. In the 15th century, when a waiter asked you to ‘foot the bill’, what he wanted you to do was to add up the figures and make sure that the total at the bottom or the foot of the bill was correct. The expression ‘foot up’, which is no longer in use, was used to mean to ‘count’ or ‘add up’. It was only in the 19th century that the expression ‘foot the bill’ began to mean what it does today.