These terms mean exactly what they say.
Prepaid means that the consumer first deposits an amount with the service provider and then uses the service. They are charged against their deposit. They can use the service as long as the service provider has a balance.
Postpaid means that the consumer first enjoys the service, then the service provider presents a bill. The customer then pays the bill.
Mobile phones offer both prepaid and postpaid options, while utilities like water, electricity, etc. are usually post paid.