Two clearly related meanings:
1) the number seven; this is a number of special significance in Judaism, as a unit of time. Examples are the seven days of the week, with the seventh day of the week, the Shabbat, being the Holy Day. Some other examples are the seven Shemittah cycles of seven years each, followed by the “Yovel,” or Jubilee Year. Contracting in time again, there are the seven weeks of Sefirat HaOmer, followed by the fiftieth day, the Holiday of Shavuot.
2) as in to “sit shivah.” Here also, the number seven is significant. It is the number of days, decreed by the Creator of Man, to be appropriate for a person to devote 100% of his or her time and energy and concentration, or as much as possible, to mourning for a loved one.