This isn't mine, but I own one of these and I have no idea what it is. With the spike attached it looks like a marking gauge of some sort.
It appears to be a base holding a scribe. Normally they are used to hold indicators (which are like touch sensors that measure how far the arm is deflected from their neutral position). You mount whatever you want on the post.
This particular style is apparently called a "surface gauge". I know them as universal bases, indicator bases, holders, etc. but those are apparently a different style. I've never seen one actually used with a scribe; Always an indicator.
Basically a base with an adjustable vertical post that you mount measuring devices to. The base is ground flat and you place it on a surface plate or machine table. You slide it around.
For example, you can check to see if two things are the same height by sliding an indicator between the two pieces and seeing of the dial reads the same, or if a horizontal beam/rod or surface is flat and parallel by sliding an indicator along the piece, or if something is round and by finding the high spot, zeroing the dial, then spinning it in the lathe or rotary table or indexing head and seeing if it the dial moves.
I am not sure what you are supposed to do with the scribe though. Seems super imprecise, has no give to climb onto higher surfaces...it just crashes and leaves marks, and no way to tell if you are touching a surface you have slid over or if it is imperceptibly lower. Way more useful with an indicator...and surface plate or machine table.
The base currently looks detached from the post and is just laid down and resting on top.