We count in base-10, cause we have 10 fingers. Base-10 means 10 numbers, 0-9.
If human beings had 13 fingers, we would be counting with 13 numbers.
A well known base-x that's not base-10 is base-2, which is the Binary Number system. 0, 1, 10, 11, 100, 101, 110, 111, ...
I don't know how...