As a professional person, you have a duty of care to your clients (both legally and morally). You have a responsibility not to cause damage to others that could reasonably be foreseen and avoided.

Your client is paying for better-than-the-average-man-in-the-street levels of expertise in your particular field. If your professional service fails to deliver what they wanted, or worse, damages them or their business, they can sue you for their losses.

So, in the context of professional indemnity insurance, negligence means a failure to carry out the duty of care you owe your client (with that failure causing them financial loss). Damage your client suffers as a result of your work could and should have been reasonably avoided by you. If that’s not the case, you’re deemed to have been negligent.