'retained earning' basically means the money a company makes in profit that it doesn't give to its owners (shareholder).
When a large company makes a profit, it has to decide what it wants to do with the money. Normally, companies give some of this profit to their owners (who are called shareholders). This is called a 'dividend', an extra payment.
But often companies keep (or retain) some of this profit. This is called 'retained earnings'. Normally, companies use the money they keep as 'retained earnings' to reinvest in the company (e.g. to buy machinery, other companies, buildings etc...), to save for the future or to pay off debts and loans that it has.
Up until recently, the tech company 'Apple' never gave any of the profit it made to the owners of the company (the shareholders) as a dividend. Its 'retained earning' were 100% of its profits.
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