Engineers can repair damaged buildings and reinforce barricades to a stronger point than any other class. Non-Engineers can make some repairs too, but they require a toolbox and cannot fully repair buildings. Engineers on the other hand can fully repair buildings (with the purchase of the Reconstruction skill), and do not need a toolbox to make repairs.
Engineers are critical to human victory. Engineers repair ruins create by strong zombies. As the round goes on, ruins are created more quickly and Engineers must repair them to stop the city from becoming completely ruined.