By default, most URLs are routed via BrowserStack’s network. Just the hosts which can’t be resolved publicly are resolved via your network.
If this feature is enabled, a secure connection is created between your machine and BrowserStack’s remote machines. All public and private URLs are resolved via your network and the information is passed back to BrowserStack via the secure connection.
The multiple hops involved in this process, increase the response time for each page load and interaction. Hence testing may be slower.
For more details on the internals refer here.