Double-entry bookkeeping records every transaction in at least two accounts, so that total debits always equal total credits. That single rule is what keeps a balance sheet balanced.
Assets equal liabilities plus equity because every entry that raises one side raises the other by the same amount, or shifts value between two accounts on the same side. A journal entry is double-entry in its rawest form — you name the accounts and the amounts yourself, and QuickBooks refuses to save the entry until the two columns match to the penny.
This is why an entry is never a single number. Buying equipment for cash does not just increase equipment; it also decreases cash. Taking a loan increases cash and increases a liability. Every economic event has two sides, and the journal entry is the place where you state both explicitly.
The rule traces back to the accounting equation — assets equal liabilities plus equity. Every valid entry keeps that equation true, which is why the sum of all debits in the ledger always equals the sum of all credits. When a trial balance does not tie out to zero, a broken or one-sided journal entry is one of the first suspects, because the standard forms cannot create an unbalanced entry but a careless manual one sometimes can.