As he states in the patent text:
The practice of removing hairs from the axilla is, at the present time, becoming more predominant and,.in order to accomplish this purpose, he ordinary safety razor is sometimes 'employed but has been found more or less unsatisfactory owing to the fact that access ca mot readily be obtained to the curvature o the arm pit to remove the hairs therefrom with the straight edge blades commonly used.If you're not steady in anatomical latin, axilla simply means armpit.
The invention itself isn't too complicated; a semicircular single edge safety razor with a curvature shaped to fit the armpit - however it is interesting in that it has no top cap, but uses two tabs fitting in corresponding slots cut in the blade and bottom plate to hold the blade secure, and a cup or ring to hold two halves of the handle together. Hopefully that is clearer from the drawing than from the text.
...having a handle with threaded orifice, a flexible slotted circular blade provided with slot with parallel edges and a series of elliptical openings placed radially in said blade, a circular head provided with guard teeth and special guard portion integral therewith to cover slot in Blade, a slightly curved circular raised portion, and an elliptical raised portion all integral therewith, a circular clamping cap member provided with a slightly depressed circular portion and a threaded stem for screwing into threaded orifice provided with handle, substantially as described.