I found my Conrete Technology textbook and while the authors don't mention eggs or egg shells, they do state that animal fats and 'organic compounds' are added to cement in order to either retard the set rate (slow the cure time down) and lengthen the time the mortar can be worked, and as an air-entrainment agent. Air entrainment helps prevent frost/ freezing damage. A retarder slows down the 'rate of hydration'. These are used to increase the working time on a pour, and in the case of large concrete projects, reduce the amount of heat generated by the hydration. In this last case, hydro dams need these additives because there is so much heat generated inside a large mass of concrete, the heat itself can damage the process of 1: the curing of the concrete and 2: cause too much expansion/ contraction and damage the reinforcement.
Slowing down the setting time can help prevent what are known as "cold joints"- where part of the mass has set before the next pour has time to bond physically and chemically with the first pour.
Cold joints can, and does, lead to cracking if stresses are applied to the concrete. And leaks: something you don't want in either hydro dams or house foundations.
I'm guessing that eggs could be considered as both 'organic matter' and animal fats.
An added bonus might be that the addition of these agents also helps the mix spread out a little better when worked with a trowel. That's desirable if you're laying down tilework.
Sugar is also a retarding agent: if you want an exposed aggregate finish to, say, your sidewalks, you pour the concrete and screed it, then dust the top with sugar (brown sugar, according to my former employer.)
After the un-sugared concrete has set (the time varies depending on the weather), you hose off the top of the sidewalk and have exposed pebbles and a less slippery finish. :-)