For a Caravan bringing Food and establishing a food route:
-The destination immediately gets half of its total food capacity filled (not sure if there's any penalty for the departure city).
-The destination gets 1 extra Food per turn, which is deducted from the city that built the Caravan
Also, a city can only have one food route with another city, so if you deliver another Caravan, the city will still only get 1 extra fpt. However, both give an immediate bonus to the city's existing stockpiles.