A non-proxy-aware client, in this context, is a client that makes HTTP requests but has no easy way to configure proxy options, or has no proxy support at all.
Common examples of non-proxy-aware clients are thick client applications or browser plugins that do not use the browser's proxy options. Burp's support for invisible proxying allows non-proxy-aware clients to connect directly to a proxy listener. This allows Burp to intercept and modify traffic based on target mappings.
Architecturally, this works by setting up a local DNS entry for the remote target that the non-proxy-aware client communicates with. This DNS entry can be made in the local hosts file, as follows:
127.0.0.1 example.org
The client ...