originally "summoning of a person into court to warrant the title to a property;" see vouch. Meaning "receipt from a business transaction" is first attested 1696; sense of "document which can be exchanged for goods or services" is attested from 1947.
A credit of a certain monetary value that can be used only for a specified purpose, such as to pay for housing or for food. Food stamps are a kind of voucher.
Note: Some economists believe that goods and services supplied by the government would be provided more efficiently if vouchers that could be spent only on such goods and services were given to citizens, and private business competed to provide those goods and services.