Number is an idea, concept, or thought indicating how many or how much.
Numeral is a representation of the concept.
For example "3" is a numeral representing the concept of "three-ness."
from math.net
"The concept of number is so abstract that a general mathematical definition has not been written for this term. Mathematicians worked for many, many years to find the words to define number accurately. Finally, they decided that the best way was to use a specific example. Although many people use the word number to mean numeral, they are not the same. Numerals are used to represent numbers, and one number can be represented with many different numerals. For example, some of the ways to represent three are 3, III (Roman numerals), and 2 + 1."
Think about it: There is an infinite array of representations of "three-ness."