A hole in a wood door is usually a puncture through a hollow-core skin or a chunk missing from a solid slab. Patch method depends on which door you have.
Hollow-core doors
Expanding foam can stabilize a small puncture: mask, fill lightly, cure, trim flush, then skim with filler and sand. Larger holes need a wood or mesh backing behind the skin before filler.
Solid wood doors
Square up the damaged area, glue in a Dutchman patch with matching grain direction, plane or sand flush, then refinish.
Finish
Prime filler and bare wood. Paint doors are easier to hide; stained doors need careful color matching of the patch and surrounding stain.
Hardware holes
Old lockset holes use a faceplate-sized wood plug or filler patch, then redrill for new hardware if needed.
For more repairs like this, start in the Doors & Windows hub. If you are working through a related problem next, see How to Properly Sand Down a Wood Door: Professional Tips or Hole in a Stained Wood Door: How to Match Color Perfectly.

