There are many different 3D-printing technologies, as you can see here.
But what all 3d printing technologies have in common is that the part gets produced layer by layer. The part is designed in a computer-aided-design (CAD) software and later exported through a slicer. This slicer cuts the virtual part into 2 dimensional slices with a thickness of usually between 20 and 60 microns. For 3d printers people have at home, this is often a bit thicker but in industrial 3d printing the slices can be even thinner, depending on the technology and the material. These sliced data need to be transferred to the 3d printer and then the printing process can begin. Depending on the technology, it is important though, that a support structure is added to the part for different reasons. In metal printing the reason is heat dissipation and stability, while for printing from liquid precursor materials the reason is, that overhangs would just sink into the liquid and would never connect to the rest of the part.
Importance of support structures illustrated through a T-part:
The significant advantages additive manufacturing or 3d printing offers us are its incredible freedom of design, very short lead times, very low cost for small batch numbers, saved costs for spare part inventory and the possibility of redesigning existing parts to integrate a lot of functions at once. There are parts, that have been made traditionally from over 200 small pieces, that had to be assembled by hand into a single part, printed in one go.