Extensive is another word for a lot or "considerable" so in medical terms the word extensive could mean that the doctor has considerable or a lot of knowledge and experience in the field they are working in in medicine.
Such as a doctor or surgeon who has extensive knowledge in surgery or doctoring and knows a lot about what they're doing.
It could also mean that someone has extensive damage to their body or insides and needs surgery to repair the extensive damage.
Extensive is just another word for large amount or considerable or a lot of knowledge.