24/7 is an abbreviation which stands for "24 hours a day, 7 days a week". It is an American way of say full time.
In commerce and industry, it identifies a round-the-clock service, potentially including holidays and days that otherwise may alter limitations of work.
In BDSM it identifies a relationship that is full-time, without any 'breaks' or 'timeouts'. It would normally imply a live-together arrangement but this is not necessarily indicated. In a D/s relationship, people might meet up only occasionally or might be living together full-time but only involved in occasional play and therefore would not consider their relationship to be 24/7 D/s.
24/7/365 is sometimes also seen and has the same meaning, the 365 implying all days in the year.