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A physical via is actually a sandwich of 3 layers:
- a bottom layer rectangular pad
- a top layer rectangular pad
- and between them, a rectangular "cut"
For example: a via that connects metal-3 to metal-4 will consist of a pad on metal-3, a pad on metal-4 and a rectangle on cut-layer-3-4.
The cut rectangle represents the hole that needs to drilled through the oxide layer separating the two metal layers.
The via overhang is the amount by which the two metal pads extend beyond the cut rectangle. The overhang has to be at least a certain minimal amount for the via to be reliably manufacturable. The bigger the overhang the better the yield for the via. The manufacturing problem stems largely from alignment problems between metal masks and cut masks. If the overhang is very small, even a small misalignment between the masks will cause the cut rectangle to not be fully covered by a metal pad, which means a connectivity failure.
I think via overhang is similar to VIA enclosure by metals. When you run DRC, if the enclosure/overhang is not minimum then you will end up in DRC violation. At times we used to place a double Via & keep enclosure more than minimum. so that it will cover DFM rules as well.
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