When we see numbers in everyday life, we always see numbers that are composed of the digits 0 through 9.  This is base 10.  For instance, take the number 1234.  When you see this number you see:

(10)³ x 1 + (10)² x 2 + (10)¹ x 3 + (10)⁰ x 4

This is how you manipulate numbers in base 10.  If you were in a different base, 'b', then the highest digit in the base is 'b' - 1, and any numbers would be represented by the following:

(b)ⁿ x a + ... + (b)¹ x a' + (b)⁰ x a''. where a, a', and a'' represent different digits.

The lowest base is of course 2, since the only numbers you can have are 0 and 1.

In number sense, we see problems that deal with bases and there are many methods we can use.