A common blessing / greeting before Yom Kippur is gmar chatima tova - גמר חתימה טובה (or occasionally gmar tov גמר טוב ). I'm not sure of the origin or development of the expression, but Passing Phrase does a good job of explaining it:
Literally: A good final sealing
Idiomatically: May you be inscribed (in the Book of Life) for Good
"Gmar" comes from the root word that means to finish. Although it's not biblical, it appears quite a bit in the Talmud (Avot 2:16 Yevamot 12:6). Chatimah is also talmudic and can mean a signature or a sealing (Pessachim 104). The word "chotemet" or stamp (the ink kind, not the postal kind) is a derivative of "chatimah." Of course "tova" means good. The days of repentance are divided into two parts: The first the inscribing begins on Rosh Hashana and finishes Yom Kippur when the final "sealing" (chatima) of our fate takes place. Many sages give us a second chance - an extra 12 days until a really final sealing on Hoshana Rabba (the 7th day of Sukkot).
That is why many people finish their correspondence during this time of year by writing or saying Ktivah V'chatima Tova - "may you be inscribed and sealed for a good year." On or right before Yom Kippur, people modify that and wish "Gmar Chatima Tova." Technically you can say it means 'may your finished sealing be good' - which would be fine if you are redoing your apartment, but for the rest of us may you all have a healthy peaceful and fulfilling year.
I would add that the root גמר does appear in the Bible with the meaning of "to complete, finish, end" - see Tehillim 12:2, 138:8. We have also seen earlier that גמר is related to גמל in the sense of "to ripen, to wean" - certainly connected to the meaning "to complete". From this meaning of the root we get the words לגמרי legamrei - "completely" and the term v'gomer - וגומר , usually abbreviated as 'וגו - meaning "the conclusion (of a verse)".
The root גמר also means "to learn", and from here we get the word Gemara גמרא (also גמרה).
Klein offers a development of the meaning that works well in English as well: he finished, he concluded, he deduced, he learned.
An unrelated term that also uses the root גמר is the word גומרה gumra - "live coal", and the related verb means "to burn spices on coal." The spices placed on the coals are called mugmar מוגמר , and the Mishna in Brachot 6:6 says that after a meal they would bring the mugmar, to perfume the house. A blessing was recited on the mugmar - בורא עצי בשמים - and from here the expression "לברך על המוגמר" l'varech al hamugmar, which today means "to bring a task to a successful completion". The more common meaning of גמר replaced the less common one.