double-entry system
Suppose you keep a personal cash diary and only write down 'spent 50 on shoes'. That single note tells you money left, but not what you got for it or how your total wealth changed. The double-entry system fixes this by insisting that every transaction be recorded in at least two places, capturing both sides of the trade: what came in and what went out, or what you gained and what it cost.
The core rule is that for every transaction the total of debits (left-side entries) must equal the total of credits (right-side entries). Buy shoes for 50 cash, and you debit Shoes (or Inventory) 50 and credit Cash 50 — the asset you own changes form, but the two amounts match. This dual recording is anchored to the accounting equation, Assets = Liabilities + Equity. Because debits and credits are defined so that they keep this equation in balance after every single entry, the books carry a built-in error check: if total debits do not equal total credits, something was recorded wrong.
This is the foundation of essentially all modern business accounting, from a corner shop's notebook to a multinational's software. Its great strength is self-checking discipline and a complete picture: you can always trace where value came from and where it went. Its limit is honesty — double-entry guarantees the books balance, but balanced books can still be wrong or fraudulent if both sides of a fake entry are simply invented. It enforces arithmetic consistency, not truth.
An owner puts 10,000 dollars of her own money into a new company. Two entries are made: debit Cash 10,000 (the firm now holds the asset) and credit Owner's Equity 10,000 (the firm owes that value to her). Assets and equity both rise by 10,000, so the equation stays balanced.
Every transaction touches at least two accounts, with debits equal to credits.
Balanced books are not the same as correct books. Double-entry catches arithmetic mistakes, not lies, omissions, or amounts posted to the wrong (but still balancing) account.