Gmar Chatimah Tova - 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.