A spacial derivativeis a measure of how a quantity is changing in space. This is in contrast to a temporal derivative which would be a measure of how a quantity is changing in time.
For instance, is you placed a metal bar with one end in ice water, and the other end in boiling water, you could measure the temperature along the bar. The temperature would be different at each point along the bar. The rate of change of this temperature along the bar is a spacial derivative.
(A temporal derivative would be if you took a hot piece of metal and put one end in ice, then measured the temperature at the other end over time, and found the rate at which it cools down.)
In mathematics it is usual, if given some function F, to denote spacial derivatives as dF/dx, dF/dy, dF/dz, or Fx, Fy, Fz, when dealing with normal Cartesian coordinates.