What is the name of the physics concept where water runs back under the edge of the roofing? Is it just surface tension? I work as an apprentice roofer and I'm interested in the why of things. Nobody I have asked can confidently answer this question so here I am.
This diagram shows the phenomenon:

The image is from this site. These are apparently called ice dams.
 A: It seems capillary action to me.
There is a source of water outside (ice), and an empty space inside. It is the same principle that water can be transported from a full glass to an empty one through a straw bridge, until both levels are equal.
This question shows the principle.
A: Looking at the diagram, I would suggest what is happening is that the "ice dam" effectively introduces an abnormal weir which then retains standing water on the tiled area, and disrupts the normal mechanics of a tiled roof which requires water to be constantly drained downwards from the surface to keep the loft cavity dry.
Tiled roofs are not actually watertight structures. It is simply by careful arrangement of the tile, and a sufficient incline, that water tends to roll consistently off the outside of the tile due to gravity, rather than working its way under and across (or up) the tile to an edge that will conduct water inside.
Most roofs also have an inner layer of felt that works in much the same way as the tile, which isn't as mechanically strong and durable as the tiles, but provides better draughtproofing behind the tiles (to control driving wind from forcing water into the tiles against gravity, rather than draining down), and the felt also conducts away any smaller drips that do occasionally get inside.
Again, if the "ice dam" blocks the drainage of the felt (as it is liable to do if the foundation of the ice is in the guttering), then this too will eventually leak into the loft area.
