Answer:
   
   One of the things that traditional Jews are prohibited from doing on
   Shabbat is "work"; more specifically, the hebrew word "melachah".
   
   Most people hear that Jews cannot work on Shabbat, and think of the
   English sense: physical labor, employment, jobs. Under this
   definition, tearing, opening the refrigerator, cooking, etc. would be
   permitted, but a Rabbi leading a service would not be permitted.
   However, Jewish law prohibits the former and permits the latter. This
   is because traditional Judaism does not prohibit "work" in the modern
   sense; the Torah prohibits "melachah", often translated as "work".
   
   Melachah generally refers to the kind of work that is creative, or
   that exercises control or dominion over your environment. The best
   example of melachah is the work of creating the universe, which G-d
   ceased from on the seventh day (and is a reason we observe Shabbat).
   Just as G-d rested from the work of creation, so we too rest on
   shabbat from creation.
   
   The word melachah is rarely used in the Torah outside of the context
   of Shabbat and holy day restrictions. The only other repeated use of
   the word is in the discussion of the building of the sanctuary and its
   vessels in the wilderness (Exodus 31:35-38). Notably, the Shabbat
   restrictions are reiterated during this discussion (Ex. 31:13), thus
   we can infer that the work of creating the sanctuary had to be stopped
   for Shabbat. From this, the rabbis concluded that the work prohibited
   on Shabbat is the same as the work of creating the sanctuary. They
   found 39 categories of forbidden acts, all of which are types of work
   that were needed to build the sanctuary:
    1. Sowing
    2. Plowing
    3. Reaping
    4. Binding sheaves
    5. Threshing
    6. Winnowing
    7. Selecting
    8. Grinding
    9. Sifting
   10. Kneading
   11. Baking
   12. Shearing wool
   13. Washing wool
   14. Beating wool
   15. Dyeing wool
   16. Spinning
   17. Weaving
   18. Making two loops 19.
   19. Weaving two threads
   20. Separating two threads
   21. Tying
   22. Untying
   23. Sewing two stitches
   24. Tearing
   25. Trapping
   26. Slaughtering
   27. Flaying
   28. Salting meat
   29. Curing hide
   30. Scraping hide
   31. Cutting hide up
   32. Writing two letters
   33. Erasing two letters
   34. Building
   35. Tearing a building down
   36. Extinguishing a fire
   37. Kindling a fire
   38. Hitting with a hammer
   39. Taking an object from the private domain to the public, or
       transporting an object in the public domain. (Mishnah Shabbat,
       7:2)
       
   As a result, all of these tasks are prohibited on Shabbat.
   Additionally prohibited is any task that operates by the same
   principle or has the same purpose (for example, driving a car uses an
   internal combusion engine, which creates fire). In addition, the
   rabbis have prohibited coming into contact with any implement that
   could be used for one of the above purposes (for example, you may not
   touch a hammer or a pencil), travel, buying and selling, and other
   weekday tasks that would interfere with the spirit of Shabbat.
   
   Let's look at one of these as an example: The lighting of fire. We
   don't do it, simply put, because G-d said so -- Exodus 31:13. "You
   shall not kindle fire in any of your communities on the Shabbat day."
   What can we learn from this? From the phrasing, it would seem that G-d
   had to make a point of telling us that this law applies even when not
   living in Israel. Why would we think it was only connected to living
   in Israel? As noted above, there are actually 39 types of activities
   prohibited on Shabbat. Lighting fires is only one of them; the others
   are extrapolated from context. Why was it mentioned separately? The
   way the laws of exegesis work, if all 39 were derived by the same
   derashah, the same oddity in the text, then all 39 would be the same
   prohibition. Someone who violates more than one would have committed
   only one sin.
   
   R' Akiva explains (Pesachim 5b) that by specifying one separately, it
   shows that all 39 are distinct. They are related to the 39 activities
   required to construct the Tabernacle. This connection is implied by
   the juxtaposition of the two topics -- Shabbos work and building the
   Tabernacle -- in the book of Exodus, as well as the fact that both
   speak of "melachah" or "meleches avodah" [melachah of avodah, losing
   yourself in construction]. This connection to construction follows
   through to the laws.
   
   For example, tearing is one of the 39. However, the Torah's
   prohibition only includes tearing as part of repairing or to measure
   out a portion. To do so just to destroy is not Torahitically
   prohibited.
   
   The philosophical connection is implied by the number 39, particularly
   as the mishnah describes it as "40 missing 1". 40 is associated with
   creation, as G-d created the world through 10 pronouncements, each of
   which had 4 aspects. So, there are 40 acts of creation whose absence
   is commemorated on Shabbos. Of the 40, one is ex nihilo which is
   prohibited by the conservation laws of physics. So only 39 are
   prohibited by the laws of Shabbat -- "40 missing one". One of those 39
   is kindling. So, when we rest from kindling fires on Shabbat, we do so
   in part because it corresponds to some aspect of creation, be it the
   creation of light on day 1, of the sun and stars on day 4, or some
   step whose connection is less obvious.