Open Tiles are tiles that are located inside a settlement that do not contain resources. Each settlement a player creates will contain 8 open tiles around the Village Centre which can be built on with any type of building except those designed for resource tiles (e.g. quarries, logging camps, farms, etc). Structures that can be on open tiles include watchtowers, barracks, and libraries.
However, with certain technological advances you can treat tiles with resources on them as open tiles. For example, with Forest construction in the Classical Age you build most buildings in forest, with hill construction in the Feudal Age you can build on hills, and with grass and sea construction in the Renaissance Age you can building on those tiles as well. This allows you to expand you city at the cost of a resource tile.