Re-entrant would also be where an ISR calls a function.
Say you are in the middle of a Serial.print. A timer interrupt fires. Inside the timer you do a Serial.print (a bad idea, I know). Then the Serial.print function is "re entered". And say inside Serial.print it keeps a variable (eg. for working out how to convert a float). That variable is now changed by the re-entry. So the original one (the one that got interrupted) is now corrupted.
This is another reason why you should keep interrupt service routines short. And why those people that try to work around Serial.print "not working" inside an ISR by adding a line to turn interrupts on, are really shooting themselves in the foot.