- "Instrumental or mechanical science is the noblest and, above all others, the most useful."
– Leonardo da Vinci
Engineering is the next step in practical building. Thanks to it, and mathematics, men learn to design complex structures and machines without having to actually build them to see them working. This opens up an infinite universe of possibilities and allows many surprising technological advancements, such as more efficient movement on roads by building bridges over rivers (which eliminates the river-crossing movement penalty), or transportation of water over large distances thanks to the Aqueduct systems.
This technology is lower on the tree, near many of the more militant pieces from this era.
Workers also learn how to create Forts. They preclude other tile improvements in the hex, but they make it easier for military units to hold the line against incoming forces.
Take Engineering to push your civilization toward major defensive technologies like Machinery (for Crossbowmen) and Physics (for Trebuchets). If you're holding off a major foe, this is absolutely the best route to take.
Engineering is the science (or art perhaps) of designing complex materials, structures, devices, and systems. In modern parlance it has a fairly wide reach - bioengineers design cells, software engineers create computer programs, and so forth - but historically the term was applied to the construction of physical stuff, like machines, bridges, railroads, factories, and so forth. (Originally the term "engineer" referred specifically to those who created military engines.)
Engineering came into its own in the 19th century, as countries around the world embarked on huge construction projects. Completed by the French in 1869, the Suez Canal connected the Mediterranean Sea and the Red Sea, making it possible to sail from Europe to India without the long and arduous journey around Africa. The United States completed the transcontinental railroad in the same year, and the Brooklyn Bridge was constructed in 1883.