If you are a teenager or young adult, then probably check balancing is less important. Those people typically only have a few charges on their checking account per week - if that. Thus it is easy to keep track in your head of the withdrawls done during the day/week and then that memorized information can be easilly checked online.
But that is a bad, bad habit to get into. Once you are in the real world, you might have 10-20 withdrawls in a day. Are you going to remember each and every one of them? Are you going to be able to check online every day to be certain everything is perfect before you forget? You will likely reach a point in your life where the answer is no to at least one of those questions. That is where checkbook balancing comes in.
It is a simple task that takes just a few minutes per month. (1) you write down everything deposited / withdrawn from your account. To make things even easier, there are duplicate checks available so you don't even have to take the time to write down the checks yourself. (2) you add them up and see if it matches what the bank says is in your account. (3) If they don't match - which is quite common - you go to the bank and get your money back. You have very little time to do so otherwise the bank legally keeps your money - which could easilly be hundreds of dollars lost if not more.
Example of a common problem: Suppose you are in the middle of a great vacation and internet access isn't on your mind. You write a check for $56.00. For some reason, the teller who cashes the check transposed the numbers and withdraws $65 from your account and transfers $65 into the store's account. As far as the bank is concerned, everything balances ($65 removed from one place and $65 deposited in another) and the bank will never know. When you get back from vacation 2 weeks later, will you remember each and every withdrawl and not accidently transpose the numbers in your head? Or will you have that $56 written down so you know you got screwed by $9?