Can someone explain double spending to me?
No you cannot. When you try to send a transaction to the chain which is not allowed by the chain (so sending more coins then you own) results in a invalid transaction. The case now is that your program didn't process your recent transactions, and therefor thinks that there are more bitcoin in your wallet then there really are. Otherwise it would be far to easy to doublespend: just reinstall Bitcoin Core and have a wallet which held a lot of BTC prior a specific date. If you are interested in reading more about doublespending (which I think you are not, just wanted to know if you were possible right now) you can read this.