The core idea is that money always comes from somewhere and goes somewhere. Every transaction therefore touches at least two accounts: one is debited and another is credited by the same amount. When you total all debits and all credits, they must be equal — if they are not, something was recorded wrong.
This self-checking property is why double-entry has been the standard for centuries. It is also what makes it possible to produce a balance sheet and an income statement that actually reconcile, rather than a single running list of amounts.
Modern accounting software applies double-entry behind the scenes, so you record a plain-language transaction and the debits and credits are posted automatically. The discipline still matters: it is what lets your reports be trusted.