Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. In contrast, simple interest is calculated only on the principal. The quote attributed to Einstein — 'compound interest is the eighth wonder of the world; he who understands it, earns it; he who doesn't, pays it' — captures the dual nature of compounding: it works powerfully in your favour when saving and investing, and against you when in debt.
£1,000 at 5% annual interest: after year 1 = £1,050. Year 2 interest calculated on £1,050 = £52.50. After 20 years = approximately £2,653. After 40 years = approximately £7,040. The later years produce exponentially more return than the early years — this is why starting early produces dramatically better outcomes than starting later with larger amounts.
The same mechanism works against borrowers. Credit card debt at 25% interest: £1,000 unpaid for 10 years with no payments = approximately £9,313 owed. This is why paying only the minimum credit card payment produces very slow debt reduction.