This is similar to phraseology here in the U.S. with regard to clearances. Here we say "rest of route unchanged." Same thing as "balance unchanged." The controller issues an amended clearance up to a certain waypoint and then leaves the rest of the route unchanged. That's all it means.
Actually you might find that "Balanced Unchanged" (in Canada anyway) refers to more than just the route remaining unchanged. It refers to an entire previously issued clearance.
Clearances include squawk codes, altitudes, holding instructions, expect further clearance times, noise abatment procedures, SIDs (Standard Instrument Departure Procedures) and other specifics (including the route).
"Balanced Unchanged" is used after a small section of an entire clearance is altered in some way, and it relieves the controller of repeating each and every detail of that entire clearance.
Hope this helps.