Re: when you look at the flight of a space shuttle on the board of nasa you see

A ground trace or ground track is the path you would
have to follow on Earth, i.e. on the ground, in order
to be as close to a satellite or spacecraft as
possible.  Imagine you're trying to listen to a very
weak broadcast from a particular satellite -- the
ground track would be the path you should follow to get
the best reception.

Such a ground track is usually plotted on a mercator
projection, see liftoff.msfc.nasa.gov/academy/rocket_sci/orbmech/mercator.html
you can find many of these plots at eol.jsc.nasa.gov/map_images/

It may also help you to get out a map of the world or,
even better, a globe if you have one. An excellent
web-based tool for understanding this is at 
liftoff.msfc.nasa.gov/RealTime/JTrack/3D/JTrack3D.html

For the sake of argument, let us suppose that Earth
does not spin.   And, let's begin with a satellite that
has a circular orbit directly above the equator and
that the satellite passes over, say, Ecuador (in South
America) every ninety minutes.  The ground track for
our imaginary satellite will be the equator (zero
degrees latitude).  In other words, the closest point
to the satellite would always be on the equator.  

Now, let's take that orbit and tilt it a little so that
it no longer passes over Ecuador, but Uruguay (about 33
degrees south of the equator on the east coast
of South America).  Our satellite's orbit is still a
circle and gravity requires that the center of that
circle must still pass through the center of Earth. 
This means that on the other side of Earth, our
satellite must pass over South Korea (about 33 degrees
north of the equator).

This means that the ground trace of our satellite would
pass through Uruguay, then go around Earth and pass
through South Korea.  Remember, the ground trace
follows a path on Earth for which you are always as
close to the satellite as you can be.  When you draw a
nice smooth line under this orbit you'll find that it
makes that same sort of wavy pattern you've seen
before.

Let us no longer suppose that Earth does not spin.  If
our satellite is in a relatively low orbit, like the
space shuttle's typical orbit, then our satellite will
make its way once around the world about every 90
minutes.  This means that after every 4 loops around
Earth, 6 hours have gone by -- Earth has made a
quarter-turn.  Our satellite's orbit does not rotate
with Earth (gravity pushes and pulls to and fro, never
sideways) so after these 4 loops we'll find that our
ground track doesn't go through Uruguay or South Korea,
anymore!  So, over the course of one loop, our
satellite's ground trace shifts about 22.5 degrees (90
minutes is to 24 hours as 22.5 degrees is to 360
degrees)

An excellent web-based tool for understanding this is
at liftoff.msfc.nasa.gov/RealTime/JTrack/3D/JTrack3D.html

When the J-Track 3D window opens, click on "View" and
select "Ground Trace".  Click on "Satellite" and select
"Select" -- this will give you another window where you
may choose a satellite to view, under the "Types" menu,
choose "Human Crew" and select "STATION"  At this
point, you should see a red path indicating the
International Space Station's orbit around Earth and an
orange path on Earth.  The orange path is the ground
trace.

You can also view ground traces with J-Track at 
liftoff.msfc.nasa.gov/RealTime/JTrack/Spacecraft.html