How important are check sequence numbers?

There are three sets of numbers on the check. I understand the ABA routing number and the account number but the third number is a four-digit check number that is incremented for each check, starting at 1001. How important is this number? Does it matter if the numbers aren't continuous with respect to my previous checkbook (the previous checkbook had sequence numbers in the 9000s)? Is this number only for my own convenience? What happens if, for whatever reason, I have two checks with the same number? What if I jump from check 1001 to 1100?