Epacts are used to find the date in the lunar calendar from the date in the common solar calendar.
If a solar and lunar year start on the same day, then after one year, the start of the solar year is 11 days after the start of the lunar year; after two years, it is 22 days after. These excess days are epacts, and are added to the day of the solar year to determine the day of the lunar year.
Whenever the epact reaches or exceeds 30, an extra (embolismic or intercalary) month is inserted into the lunar calendar, and the epact is reduced by 30.
Leap days extend both the solar and lunar year, so they do not affect epact calculations for any other dates.
After 19 years the lunations should fall the same way in the solar years, so the epact should repeat after 19 years. However, 19 × 11 = 209 , and this is not an integer multiple of the full cycle of 30 epact numbers (209 modulo 30 = 29, not 0). So after 19 years the epact must be corrected by +1 in order for the cycle to repeat over 19 years. This is the saltus lunae (jump of the moon). The sequence number of the year in the 19-year cycle is called the Golden Number. The extra 209 days fill 7 embolismic months, for a total of 19×12 + 7 = 235 lunations.
In the Gregorian calendar, there are 30 possible values for the epact. Epacts always are computed modulo 30, and always indicate the New Moon. Therefore the epacts are in units of of a lunation (also called a tithi). However a lunation is less than 30 days, so the epact unit is less than a full day.
This can also be understood from the following fact (please read computus for an explanation of the terms and procedures referred to here): Almost half of the lunations last only 29 days. In the Calendarium 12 days in the year have a double epact label (xxiv,25 and xxvi,25; one of these is used depending on the Golden Number). Therefore the correction of the epact by one unit does not always result in a shift of all dates of the New Moon (and Full Moon) by one day: for epacts 25 in short lunar months there is no difference. So the epact corrections are less than one day on average, and therefore the epact itself is not measured in calendar days.
It may be argued that Lilius applied the "solar equations" in order to bring the lunar calendar back in sync with the original Julian calendar; the "lunar equations" would then make a long-term correction to the approximate Metonic relation between the Julian year and the mean lunation. However, the "lunar equations" are applied at the begin of Gregorian years, not Julian years. The Gregorian epact tables have a period of 5,700,000 years. When counting epacts as days, the lunar calendar does not repeat however with this period, neither in this many Gregorian nor in Julian years.