Great question — answering as the UphillTech team:
This answer assumes the US-type of pancake. There are some pancake recipes with no egg at all. So the question is, what does the egg do in a pancake recipe? It contributes soem fat and emulsifiers from the yolk, some water, and a bunch of protein (mostly from the whites). This will add structure to the pancake, some eggy flavor and richness, and perhaps somewhat mitigate the danger of toughening the pancake through over mixing, by inhibiting gluten formation (mostly due to the fat and lecithin from the yolk). However, as you have already discovered, the egg is not completely essential to the pancake, which basically a griddled quick bread, and can easily get all of the structure it needs...
Full answer by SAJ14SAJ: https://cooking.stackexchange.com/a/30161 (CC BY-SA 3.0).
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