The word "vouch" originates from Anglo-Saxon and Old French word "voucher", meaning "to summon" or "to call", which in turn comes from the Latin "vocare", meaning "to call".   It is related to the Latin word for "voice" and comes from a Proto-Indo-European root meaning "to speak". The original meaning referred to calling someone to court to prove a title, and it evolved to mean "to declare or assert" and later "to support with proof or evidence". 

According to the Oxford English Dictionary (OED), the verb "vouch" has been used in English since the Middle English period (around the 14th century), with the earliest evidence found from 1303 in the writing of Robert Mannyng. The noun form "vouch" appeared later, with the earliest evidence in the early 1600s (1610). 

Examples of "vouch" used in a sentence: 
"They will vouch for the fact that it is not an easy place to go." 
"I can honestly vouch for the fact that what they're saying about ij is not true." 
"She walks three miles a day and can vouch for her own product." 
"Often, the family and friends who could vouch for them are dead." 
"Often, the family and friends who could vouch for them are dead." 
"I've read the text of his post and can vouch for its scientific accuracy."
"Those we contacted vouch for the borrower and agree to help pay back the company if the borrower can't." 
" BuzzFeed published his comments in full while acknowledging that it could not vouch for its veracity."

Of course we also have the noun voucher, which is something we all like to receive either physically or digitally at this time of the year. It's use is similar to the Old French to summon or to call (Thanks @Bill W), in that a modern voucher is a summons or a call to the supplier of the voucher to provide the value stated on the voucher, usually some form of discount.

Just the facts:

VOUCH Definition & Meaning - Merriam-Webster

VOUCH Synonyms: 18 Similar and Opposite Words | Merriam-Webster Thesaurus