Blueprint mode allows you to plan your cities ahead, without using construction materials. In the blueprint mode every building is placed as a ghost version of a regular building, no credits or materials are used, the blueprint building has no maintenance or workforce cost. If you have all needed materials you can upgrade the ghost building to a normal one, either by clicking on the blueprint building and on the upgrade button, or by using the upgrade tool (which allows to quickly upgrade many blueprint buildings).
This mode is very useful when building farms (or other buildings using modules - like zoo or museum). After placing a blueprint of a farm, you can plan all its fields as well. When you upgrade the farm all farm fields will be built at the same time.
You need to unlock a building first to place its blueprint. You can't plan your entire city in the beginning of the game.
You can turn the blueprint mode on or off using the button in the bottom right corner of the construction menu or by pressing V. If the blueprint mode is turned off but you don't have enough construction materials, you will automatically place the blueprint version of the building, which you can later upgrade if you acquire necessary materials. If you don't like this function, you can completely disable the blueprint mode in the settings menu.