When architects and builders talk of cement they usually mean Portland cement although there are others such as lime and pozzolan cements. At least since the time of the ancient Egyptians lime cements have been used in building and were still used up to the early years of this century in many countries, including Australia. Mixing the quicklime with water produces slaked lime or hydrated lime, calcium hydroxide. If the hydrated lime and sand are mixed with water to form a paste this can be used as a mortar for joining bricks or other masonry. The setting of the lime mortar is caused by loss of water and hardening takes place through the reaction of the hydrated lime with atmospheric carbon dioxide to form calcium carbonate crystals which bind the mass together.
Lime mortar is attacked by acids which make it less durable and prone to erosion.
The Romans were great builders and invented concrete. They discovered that by adding volcanic ash to lime cement that a much stronger cement was produced. Such cements are called pozzolan cements. It does not by itself act like a cement but with water it reacts with lime or slaked lime to form a hydrated gel called tobermorite. The gel, and others like it, bond the mass together.