I am familiar with "seal the deal" only as an expression.
The word seal, according to the Oxford English Dictionary, has been in use since the 1200s:
A device (e.g. a heraldic or emblematic design, a letter, word, or sentence) impressed on a piece of wax or other plastic material adhering or attached by cords or parchment slips to a document as evidence of authenticity or attestation; also, the piece of wax, etc. bearing this impressed device.
In modern (legal) practice the seal is often represented by a coloured wafer following the signature of each of the parties.
Leaden seals were used by the Popes, the Eastern Emperors, and certain other high dignitaries.
So people literally put seals on deals; this was the older form of certifying a document. Now, as the OED says, there are still seals in use--represented by a colored wafer. I am not sure in how many countries this is practiced, but it seems that now there are both literal seals (the wafers, though they are not necessarily imprinted wax any more) and metaphorical seals (to say you "sealed the deal" even though there aren't seals impressed on them).
"Seal the deal" would mean "sign the contract" in today's language.
Early in the Middles Ages, few people could write (even many nobles couldn't). So they would "sign" papers by "stamping" them with their noble or family "seals" (emblems) that had been dipped in ink. As long as they maintained sole possession of such seals (which were hard to manufacture), their "signatures" couldn't be counterfeited.
The use of "seal" in this context reflects ancient practice. One easily accessible example: The Biblical book of Jeremiah recounts a land deal as follows: "I signed the deed, sealed it, got witnesses, and weighed the money on scales. Then I took the sealed deed of purchase, containing the terms and conditions, and the open copy, and I gave the deed of purchase to Baruch son of Neriah.... I charged Baruch, saying, "Thus says the Lord of hosts, the God of Israel: Take these deeds, both this sealed deed of purchase and this open deed, and put them in an earthenware jar, in order that they many last for a long time. For thus says the Lord of hosts, the God of Israel: Houses and fields and vineyards shall again be bought in this land." (See Jeremiah 32:6-15 for the full story. The text above is from the New Revised Standard Version of the Bible. Other versions might differ slightly in some details but the "sealed deed" is consistent.)
