A crazy person; a crank.
There are countless words in the language that began as two-word terms, later to become hyphenated and later still to merge into a single word, for example, 'zigzag', 'forewarned', 'ninepence' etc. Crackpot is on that list.
If you go about researching the origin of 'crackpot' it won't take long to come up with the village of Crackpot, in Swaledale, Yorkshire. This is the site of the imposing ruined farmstead, Crackpot Hall. This name long predates the use of the term 'crackpot' meaning crazed, as it dates from at least the 12th century, before which the region had been taken over by Viking insurgents. Inviting as the idea might be, the Vikings didn't turn up there and decide that the locals were mad and name the place accordingly. At that time the village was called Crakepot, which derives from the Norse terms 'kraka', a crake or crow and 'pot', a deep hole or pit - neither of which has anything to do with the current 'crazy' meaning of the word. Crackpot was merely 'the hole where crows gather'.
To discover its origins, we need to ignore the Vikings and realise that 'crackpot' is a shortened form of 'cracked-pot', which splits into its constituent parts, cracked and pot.
Cracked is itself a shortening of 'brain-cracked' (or cracked-brained'). 'Cracked' simply meant 'impaired'; 'faulty'. Both of these terms were current in the 17th century. For instance, in Randle Cotgrave's, A dictionarie of the French and English tongues, 1611, we find:
Estropié de caboche, ou de ceruelle, frantick, witlesse, braine-sicke, brain-crackt.
And in John Canne's A Necessity of Separation from the Church of England, 1634, we find:
If Mr. Bradshaw had found such a reason in Mr, Johnson's writing, he would surely have called idle head, cracked-brained, fool etc.
In the Middle Ages, 'pot' was used to mean 'skull' or 'head'; for example, this piece from Guy de Chauliac's translation of Grande Chirurgie, circa 1425:
Ye pot of ye heued
So, a 'cracked pot' was a 'faulty head' and crackpot is synonymous with our more recent terms 'numbskull', 'blockhead', 'brain-dead' etc.
The first record that I can find of the term 'crack-pot' (with a hyphen at that stage) is in a Broadside Ballad, recorded by John S Farmer in 1883:
My aunty knew lots,
and called them crack-pots.