Why do Jewish people keep the sabbath?

We believe that G-D created the world in 6 days and on the 7th day he rested. So technically Jews are supposed to not work (as defined by the Rabbi's) on Friday evenings and Saturdays.

Added:

The second reason for observing Shabbat can be found in Deuteronomy. It says,

"remember that you were a slave in the land of Egypt, and the Lord, your God brought you forth from there with a mighty hand and with an outstretched arm; therefore the Lord your God commanded you to observe the Sabbath day."

So it is also an exercise of a free people to refrain from work because they can.