Abgrenzung refers to the East German's policy (or political movement) of total separation between East Germany and West Germany. The literal translation would be 'demarcation' or 'separation' (my best bet at a real literal translation is 'off-bordering'. But don't trust my Germish). This policy did not appear as a political reality until the early 1970s -- long after the construction of the Berlin wall. Abgrenzung was the East's response to the Basic Treaty and Ostpolitik, both of which increased the contact between Easterners and Westerners. This marked the beginning of the serious attempts to make East and West Germany forever separate states.
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Here's a general outline:
1961 -- border closed, wall built.
1966-70 -- Ostpolitik helps reconnect East and West.
1971 -- Erich Honecker (East Germany's party chief) renounces the objective of a unified Germany. Abgrenzung is born.
1972 -- the Basic Treaty is signed (recognizing two separate German states, but establishing commercial, tourist, and cultural relations).
1973 -- East Germany enters into the United Nations (on it's own).
1974 -- East Germany removes all references to "the German nation", along with references to unification, from their constitution. They also reaffirm their irrevocable ties to the Soviet Union.
1989 -- Things fall apart. Including the wall.
1990 -- Reunification.