Both exist for the same reason: to record a cost in the period it relates to rather than the period it was paid in. This is what accrual accounting means in practice.
Prepaid: paid now, used later
An annual insurance premium paid in January covers twelve months. Charged entirely to January, that month carries a cost belonging to the whole year and looks far worse than it was.
Instead the payment is recorded as an asset and charged a twelfth at a time. Until it is used, it is something the business is owed — coverage not yet received — which is why it sits among assets.
Common cases: insurance premiums, annual software subscriptions, rent paid ahead, licence fees.
Accrued: used now, paid later
Work done by a subcontractor in March and invoiced in April is a March cost. Left until the invoice arrives, March overstates profit and April understates it.
The cost is recorded in March with a matching liability, and the liability clears when the invoice is paid.
Common cases: subcontractor work completed, wages earned but not yet paid at period end, utilities consumed, interest accrued on a loan.
Why it matters to a small business
Without these adjustments, monthly profit swings on the timing of payments rather than on trading, and the month with the annual insurance renewal in it looks like a bad month.
That makes month-to-month comparison meaningless, which is the main thing the statements are for.
The mirror on the revenue side
Money received for work not yet delivered is the same idea from the other direction — see deferred revenue.