As can be seen from the various responses above "The Mosaic Law" was a collective name given to a vast and complicated series of edicts given to the ancient Jewish people by divine fiat and mediated by the person of Moses. In traditional Jewish theology it signified the relationship entered into by the Israelites and the God they worshipped, Yahweh.
There are some eight seperate words that can be construed as meaning "Law" in Hebrew. The most comprehensive of these is the word "Torah" There is a certain overlapping ambiguity in the application of this word as a result of which it can have several seperate meanings. There is a sense in which it refers to the entire corpus of Mosaic literature, embodied in the first five books of the OT, however it can have a more restrictive meaning alluding to the some 600 ordinances embedded in those those five books.
Jewish theolology has long been concerned with the broad efficacy of this legal system, especially in the light of increasing impracticalities in observance. [For instance how does one celebrate the Sabbath in the North Pole, where the sun may not set for 6 months] As a consequence of this a parallel system of belief developed around a series of commentaries designed to expand and explain the "Torah" This came to be known as the "Talmud" It has been accepted by conservative scholarship that the Babylonian Talmud developed over several centuries between at least the 2nd Cent BC and the the 5th cent AD. Talmudic scholarship presently undergirds almost the entire scope of Jewish Theological investgation
For Christians, the importance of the "Mosaic Law" derives from its relationship to the epistolary revelation of the NT. There is no unanimity of opinion that can be considered authoratative enough to cover the entire range of Christian belief.
Whereas it is accepted that Christ kept the Law to perfection, the implication of this is debated. The most common Evangelical belief is that the Law, or at least its physical aspects, has thus been done away with, and the relationship between God and the believer is now through "grace" and not "works of the Law"
There is, however, a collective body of Christian believers, who form a sub-group within the Evangelical tradition who differ. This group is collectively known as the "Holiness" movement, and the denominations within this grouping are usually styled "Churches Of God" They feel that because Christ kept the Law, it does not mean that it has been removed, but that it is still operative. To varying degrees, these groups keep different aspects of the Mosaic Law, the different festivals for instance.
The SDAs suggest that the Sabbatical aspects of the Mosaic Law are still valid, along with certain dietary restictions
Another sub-family, called the Sacred Name Movement, [because they, like the WTS, emphasize the need to employ God's "name" in worship] adopt many of the more overt customs of the Mosaic Law, in fact identifying them more with Judaism than Christianity. Several of the leaders within these groups wear Jewish vestments in worship.
The WTS likes to give the impression that they, like Evangelical Christians, no longer pattern themselves after the Mosaic Law, but their emphasis on leagalism, and their almost paranoid concern with doctrinal purity belies this impression
