With professional indemnity insurance (PII) policies the insured peril is professional negligence. Professional negligence is the failure of a professional to exercise reasonable skill and care. Most professional services contracts contain either a written obligation to exercise reasonable skill and care or, if not a written term then unless a higher standard is expressed, it is likely to be implied by law.
If a professional such as a Designer designed something for a client in a way that no other designer would have designed it and then, as a result, the item designed was defective then that designer would be negligent. That is, it would be taken that the Designer did not exercise the same level of skill and care as every other designer in his profession would.
If this defective work has caused extra cost for the client then the client may recover from his designer the costs arising from his negligence. A professional indemnity policy held by the Designer would indemnify him from the negligence claim of his Client. If it is found that the Designer was negligent, then his Insurer would pay, in accordance with the terms of the PII policy in question, to the Client in respect of the relevant losses.
However, just because it turned out that something went badly wrong doesn’t always mean the professional was negligent. He is only negligent if he falls short of the standard of his peers.