The primary purpose of the slips cordon - which generally includes one to three slips and possibly a gully fieldsman - is to catch balls that have hit the edge of the bat, and moved away from the wicket-keeper. It is incredibly difficult to be a slips fielder as it requires very quick reflexes and incredibly good eyes. You can generally tell just how attacking a fielding team is by looking at the number of slips they have: none to one means very defensive, two means a little defensive, three means aggressive, four or more means very aggressive. (Of course, it also pays to look at the spread of the field: deeper fieldmen = more defensive; more fieldsmen on the leg side = more defensive.)
Occasionally, players field nine slips. This is the entire field in the slips cordon (the bowler and wicket-keeper make eleven) and is usually not very serious (ie. for the purposes of photography or to attempt to score a hat-trick) and very daring (it is easy for batsmen to hit away from the slips). However, sometimes this tactic works.
Variations of the slip include the fly slip (as mentioned above, a slip who stands further back from the wicket), the floating slip (a slip who stands somewhere in the region of third and fourth slip, and patrols the area rather than simply standing there), the leg slip (equivalent position on the opposite side of the pitch), and the fly leg slip (combination of fly and leg slip). The gully generally stands about half way between point and fourth slip, and can be a dangerous fieldsman for batsmen who enjoy late cuts.