Layer height: Layer height is the thickness of each layer a 3D printer deposits or cures, and it trades surface smoothness on sloped faces against build time.
Every 3D printing process builds a part in slices. The thinner the slice, the smaller the visible steps on curved and sloped surfaces (the staircase effect), and the more slices the part takes. FDM layer heights are usually 0.1-0.3 mm with a 0.4 mm nozzle; resin printers commonly run 0.025-0.1 mm; polymer powder bed processes sit around 0.1 mm.
What it means for the price
On FDM, halving the layer height roughly doubles the number of layers, and so roughly doubles print time for the same part, because every layer has to be traced. On DLP and MSLA resin printers, time per layer is almost fixed, so print time follows the layer count directly. A shop that lets the buyer choose a layer height should price it through time, not through a flat surcharge.
Example: an FDM part 60 mm tall has 300 layers at 0.2 mm and 600 layers at 0.1 mm. The figures are an example.
Common confusions
Layer height is not the same as detail in the plane (XY), which comes from the nozzle, laser spot or pixel size. Thin layers also do not automatically make a stronger part; layer bonding and anisotropy matter more. The slicer is where layer height is set; read how FDM print time is estimated.
Go deeper: FDM print time estimation: why volume does not predict it