1) Not to be confused with the Julian calendar, a Julian date or day number is the number of elapsed days since the beginning of a cycle of 7,980 years invented by Joseph Scaliger in 1583. The purpose of the system is to make it easy to compute an integer (whole number) difference between one calendar date and another calendar date. The 7,980 year cycle was derived by combining several traditional time cycles (solar, lunar, and a particular Roman tax cycle) for which 7,980 was a common multiple. The starting point for the first Julian cycle began on January 1, 4713 B.C. (Gregorian calendar - expressed in the ISO date format as "-4713-01-01 G") and will end on January 22, 3268 (3268-01-22 G). The following day will begin the first day of the second Julian date period (or 7,980 year cycle).
A Julian date or day number for a certain time of day on January 9, 2001, looked like this:
2451919.3423000001348555meaning 2,451,919 elapsed days since the beginning of the Julian cycle. The ".3423000001348555" represented the time of day ("15:12:54 EST").
It is not certain whether the Julian date or day number system was named after Joseph Scaliger's father, Julius Caesar Scaliger, or after the Julian calendar. Julian day numbers are widely used in astronomy.
2) Commonly in computer programming, Julian date has been corrupted to mean the number of elapsed days since the beginning of a particular year. For example, in this usage, the Julian date for the calendar date of 1998-02-28 would be day 59.