A Nyquist diagram is a way of representing the response of a feedback system of the form shown below (or similar):
______
+  
I 0> A +> O
+^ ______ 
 ______ 
   
+ B < +
______
Open Loop Gain = A
Loop Gain = AB
Closed Loop Gain = O = Forward = A
I 1  Loop 1  AB
A Nyquist diagram shows the locus of a point on the complex plane. The locus of the point uses polar coordinates to represent the negative loop gain (AB) and phase change of the system as frequency increases as shown below. It is based on a sine wave in and a sine wave out.
Im
 g = loop gain
 ph = phase
Re
\ \
 \ ph 
 \ _/
 \
 g \
 \
 o

They tend to look something like this (if you'll excuse the ascii):
Im

__ 
_/ \
/Re
/  
  /
\_  _/
\_  __/
\_____/

The most important point on this type of diagram is at (1, j0). This point helps the system designer to tell whether the system will become unstable (if it will occilate out of control). The unit circle arount this point also shows the area of positive feedback; the rest of this plane is negative feedback as defined by Black.
A system will be unstable if the locus of the system encloses the (1, j0) point like so:
Im
__ 
_/ \ 
/ \
/+Re
  
\  /
\_  _/
\_  __/
\_____/

Though in some cases the instability is limited to frequencies where the system's locus is in the left hand half plane.