A 3D printer works just like a traditional inkjet printer, only it has been modified to print in 3D, with filament instead of ink.
Basically, a 3D printer will print a design by creating the model layer by layer, building it on a bed surface from the bottom up, by depositing filament in certain places. This method is known as Fused Deposition Modeling (FDM).
The 3D printer works automatically, as it is connected to a computer that has the appropriate programming to direct the nozzle so that it deposits the material in the right spots for the right amount of time so that the result is the design that has been chosen and instructed.
So, essentially, the 3D printer is drawing many different two-dimensional cross-sectional layers, one on top of the other, using filaments of material, so that volume is slowly added and the model is created.
The filaments that the 3D printer uses instead of ink. Are molten plastic, fused together with either adhesive or with ultraviolet light. There are many different types of filament used in 3D printing, depending on the end result desired.
So, put in simpler terms, the 3D printer draws the model in material filament, over and over, slowly adding volume, so that the full model is created from the base up in multiple different layers. This also means that the bigger the model, the longer it will take because the more layers it will need. And something similar works for detail, as the more detailed the model is, the more layers it will also need in order to get them right.