These structures were homes for doves, originally built by monks to provide themselves with fresh meat through the winter.
But they were long a source of dispute with their peasant tenants, as the birds lived off the grain from their fields, so on top of their normal tithes to the church, they were being indirectly taxed also. When the monasteries were dissolved, dovecotes were often built on wealthy estates, and could be huge, and very expensive and ornate.
But with the food shortages that followed the Napoleonic wars of the early 19th century it was decided that the doves consumed far more food than they produced, so a few were kept for ornament only. This last I find a bit strange, because in today’s world, feeding cattle with corn is generally seen as a good thing, but I don’t get the maths on this.