"Finished school", in British English, means that he finished secondary school. After that, he completed a university degree (presumably a Bachelors) in business studies. In this context, "when" means "after", and "did" means "completed".

Without any further context, you would understand the phrase 'did a degree' to mean completed a course of study - probably a three/four year course at university - and graduated with a degree at the end of it.