Explanation
This is a learning trick to help you learn and remember your multiplication facts when multiplying 9 times (x) any number from 1 to 10. For example, to find 9 x 4, fold down the 4th finger from the left: 3 fingers remain to its left (the tens digit) and 6 fingers remain to its right (the ones digit), giving 36.
There's also a neat pattern in the answers themselves: see The Rule of Nines for why the two digits of any 9-times answer always add up to 9.