Not too hard to explain, actually. It's basically like writing a bad check. You have $100 in your bank account but you write two $100 checks to different vendors. You successfully double spent your $100. It's a criminal offense in most jurisdictions to knowingly do this. and banks will penalize you if you do this by accident (you can also pay for overdraft protection)

The trickier question is why double-spending is a problem for decentralized ledgers.

In the current system, your bank maintains the ledger. Your bank tells the first merchant that cashes your check that it's good, and credits their account. Your bank then tells the second merchant that your check is no good, and they don't credit the account. It's a centralized system that relies on the bank's ledger as the source of truth.

What happens if there's no centralized ledger?

You write a $100 check to Alice and a $100 check to Bob. They each maintain their own ledger. Their ledgers start off in-sync, both saying you have $100. After you spend with both Alice and Bob their ledgers become out of sync. Alice's ledger says she now has your $100, whereas Bob's ledger says he has the $100.

Now, let's say Alice and Bob then both want to pay other merchants. Whose ledger is correct? Who has the authority to determine that? Without some source of truth, why would any merchant accept the validity of either Alice or Bob's ledger?

That's the problem that Satoshi solved... a way for everyone to have consensus at all times on the state of the ledger, so that double spends can't happen.