Have you ever tried to guess how many jelly beans are in a jar? Or "guesstimated" the number of people who were at the concert last night? Number sense is your intuitive recognition of numbers and their relationships. You can tell, for instance, that one group of circles contains more shapes than another, even though you don't know the exact number. This is an ability shared with many animals, and helps them (and us, in days gone by) to survive.
These days, however, we tend to emphasize and place value on outright calculation in schools. If Jimmy has ten apples and he gives away two, how many does he have left?