To emerge or occur incidentally or unexpectedly.
The word crop has several meanings. As a noun it is a swelling on the body, or any rounded or swollen item, for example a bird's gullet, the seed head of a ripe plant or the the rear end of a horse. As a verb it means 'to cut the top or sides off' or 'to gather in' (as in cereal crops). A less well-known meaning is 'to protrude from the earth's surface'.
The context of early printed examples of the term 'crop up' doesn't help us decipher whether that 'crop' is an allusion to the growth of crops or to the 'swollen' meaning. That is because the things that were first said to have 'cropped up' were rounded items which protruded from the ground, that is, rocks.
The term 'crop up' has been used since at least the 17th century by miners, geologists etc. to refer to rocks that break the earth's surface - literally, outcrops. The Stuart nobleman Dud Dudley, in Metallum Martis, 1665, a record of mining in the English Black Country region, referred to the 'cropping up' of coal:
"The coles ascending, basseting, or as the colliers term it, cropping up even unto the superfices [surface] of the earth."
The later use of the term 'crop up' in its figurative 'emerge unexpectedly' meaning seems quite a natural progression. The Proceedings of the Royal Asiatic Society, 1832, include a citation that could easily be read as having a figurative rather than literal meaning, if it weren't for the geological context.
"Grey-wacke, and slaty limestone, conformably stratified, crop up above the ocean in the Booming isles to the north."
A more obvious figurative version appeared a few years later, in Benjamin Disraeli's Coningsby, or the new generation 1844:
"We shall have new men cropping up every session."
Coincidentally, crops still feature in the language of geologists and archaeologists, in the form of crop marks. These are the lines which are created by variations in the growth of plants caused by buried rocks or archaeological remains. Although difficult to see from the ground, crop marks materialize quite clearly when viewed from the air. They could be said, both literally and figuratively, to crop up in the landscape.
See also: come a cropper.