Whenever we want to come up with the "number of ways" that things can be arranged, we should think about how many options there are for each "choice", and then multiply them all together.
In this case, we have 8 digits to choose from, and the digits can be repeated - in other words, selecting a particular number for the 100s digit does not affect the options available for the 10s or 1s digit.
The only limitation that is given in the problem is that the number must be odd - so the 1s digit must be odd. The 100s and 10s digits wouldn't need to be limited to being odd.
So, thinking of each digit one at a time, we have 8 choices for the 100s digit. 8 choices for the 10s digit. But only 4 choices for the 1s digit, because is has to be odd (1,3,5, or 7). Multiplying those together:
(# choices for 100s digit) x (# choices for 10s digit) x (# choices for 1s digit)
8 x 8 x 4 = 256
There are 256 different 3-digit odd numbers that can be made from those 8 number choices.
I hope this helps!