The tunnels are an underground network of pathways surrounding Zion and about 30-40 miles of it's perimeter. They are primarily used by Zion Hovercrafts to fly into the Technical channels and be able to hack into the Matrix inserting redpills. The network of tunnels appears to be stretching from Zion all the way up to the surface. The only exit from the network as seen in Revolutions leads to the fetus fields, and in Final Flight Of The Osiris.
Originally, the United Nations had been drilling tunnels to create an underground network consisting of Barracks, Factories, Living space, etc., to wage war against the machines. However soon the humans' fate in the war became evident, and the tunnels were expanded and drilled down 4.3 kilometers deep into the ground to begin the construction of an underground city of Zion as the last human resort.
With time, the network was expanded, and giant pipelines were built to bring in the fuel and energy needed to build the city. The tunnels themselves were expanded, allowing for more material to be transported into Zion.
Humans have placed numerous fortresses in the tunnels to defend Zion, however with time the Sentinels have destroyed them, leaving Zion the only known manned armed base on Earth. In the timeframe that the trilogy takes place, the tunnel network is used by Zion Hovercrafts to travel to Technical channels and crop fields to hack into the Matrix and rescue redpills.