Workforce, generated by your population, is required by production buildings to operate. In Anno 1800 workforce is divided into population tiers: farmers work on farm fields while workers in factories. Every type of workforce is required to sustain your cities, your farmers can't work in advanced factories which have to employ engineers.
Every residence generates the same amount of workforce as a number of people living in it. Your island's workforce balance is displayed on the top part of the screen (screenshot needed). After hovering over specific workforce type you can learn how many people of this tier provide workforce and how many people are currently employed. In Anno 1800 unemployment has no effect on the gameplay, it is always better to have a surplus of workforce instead of a deficit.
Each production building requires a particular number of workers from specific tier to operate at 100% productivity. If there is a lack of workforce then the deficit is shared between all factories - their production time is longer and their producitivity is lower than 100%. To compensate the deficit you can adjust working conditions but it can have a negative impact on the happiness of your population.
Some items can change how much workforce your population generates or how many workers your factories need.
Surplus of workforce can be shared between different islands. Islands which have Commuter Pier built, share their workforce pools - all workforce from connected islands can be used on each island without the need to build cities on every one of them.