What does it mean to "interrupt movement"
You may interrupt the figures movement in any place between the starting point and ending point. Including the starting and ending points.

This can be argued By the official FAQ (v.2.0)


  Q:
  If a player has the
  Navigation
  tech and is moving a figure
  across water but cannot end in water, and his opponent
  stops that figure’s movement in a water square using the
  resource ability on the
  Communism
  tech, what happens?
  
  A:
  The figure stops in the water square. In this case, the
  resource ability on the
  Communism
  tech overrides the rule
  that figures cannot end their movement in water


In this case, the moving player was intented to move from the other side of the lake/river to the other side. The movement was interrupted with the spy between the starting and the ending point.



In practice, if for example my friend is attacking me in his turn, coming from 5 tiles away and says "draw your cards, I'll attack you", I would respond "hold on a second, mate. I'll got a spy in you camp.. ;).Now just say that which route you used to come over here..?". He now shows the route and I use my spy and say "This is the place where my spy came in and interrupted your movement".



The Itchis huge summary of Official and Unofficial rules and clarifications in BGG has more notes on the Communism tech.