You're right, it doesn't show your balance offline.  But it doesn't need to know your balance.  You only need that to create the transaction, which is done from the online computer.  Once the transaction is created (and a bunch of other verification data is bundled with it), the offline computer has everything it needs to know to determine "This wallet is sending X BTC to address Y with fee Z."  Then it allows you to sign it.

That's all the offline computer does:  lets you confirm the transaction details, and sign it. 

You can think of it like writing a checking that requires the signature of someone locked in a vault.  The person in the vault doesn't know how much money is in the bank account because they have no access.  But the check isn't valid without their signature.  So you go into the vault and they say "This check is sending X BTC to addr Y, is this what you intended?".  You approve, they sign it, and then you leave the vault and take the check to the bank (broadcast to the network).