A proof of concept answers a narrow question cheaply, such as whether AI can extract the right fields from your actual invoices or whether a legacy system's API exposes the data you need. It should have success criteria agreed before work starts.
For example, a proof of concept might run a few hundred past customer emails through a classifier and compare the results with how staff actually routed them. The misconception is that a successful proof of concept is nearly production-ready. It usually skips security, integrations, error handling, monitoring and training, which is where much of the real effort sits.