In parliamentary procedure, without appointing, or fixing, a day to assemble again or an adjournment without indicating a day for reconvening; as in, "The congress adjourned sine die."
When any meeting, or court-of-law, adjourns sine die (generally pronounced, sigh ni DIGH, in English), "until an unspecified date"; literally, "without a day"; it will close without appointing a day on which to appear or assemble again.
Most jurists (judges, etc.) usually say something like, "Go hence without day." which is a final adjournment or final dismissal of a case or "cause". You may notice that American judges and other legal practitioners in the United States are not actually translating the Latin correctly since they say, "without day" instead of "without a day". Apparently the term is considered obsolete in the U.K.