When my daughter was applying for fully funded scholarship (and wanted to get into the universities that had the best reputation in her field) she asked her honours supervisor and the internal examiner for recommendation to key people.
They emailed these people and said something like 'I've recommended that Sooty might approach you regarding supervision for her topic, etc, etc). After her referees had emailed the top professors, Sooty then sent along her own emails, saying that Dr Readalot had suggested she approach them, and her email included some fairly detailed paragraphs outlining her potential topic, approaches that might be taken and a couple of sources, that she had already looked at that might be useful.
So in this way 'Sooty' could set up some interviews with the potential new supervisors, meet them, etc. They were interstate- which in Australia meant plane tickets, taking some time to visit both universities and meet people etc.
After she met the advisors-she then submitted formal applications. The applications included formal references and these were completed by her honours supervisor and department head (and internal examiner) and sent to the top professors, and the universities along with all of her other material for application. Both applications were successful so she got to choose.
So the referees provided an email introduction to Sooty recommending her as a potential candidate and also breaking the ice for her and the top professors. References may have mentioned things as well-but Sooty did not mention these in her formal application only in her first email 'expression of interest'. Hope this is helpful.