Two examples may help more than a detailed explanation.
Suppose we have .000003567
Move the decimal one place to the right of the first non-zero digit and write:
3.567 x 10-6 where "6" is the number of places we moved the decimal to the right
Now suppose we have 3567
Again, move the decimal one place to the right of the first non-zero digit and write:
3.567 x 103 where "3" is the number of places we moved the decimal to the left
So....moving the decimal to the right results in a negative exponent on 10. And moving it to the left results in a positive exponent on 10.
Hope that helps.