The Web Application Proxy is part of YARN. By default it will run as part of the Resource Manager(RM), but can be configured to run in stand alone mode. The reason for the proxy is to reduce the possibility of web based attacks through YARN.
In YARN the Application Master(AM) has the responsibility to provide a web UI and to send that link to the RM. This opens up a number of potential issues. The RM runs as a trusted user, and people visiting that web address will treat it, and links it provides to them as trusted, when in reality the AM is running as a non-trusted user, and the links it gives to the RM could point to anything malicious or otherwise. The Web Application Proxy mitigates this risk by warning users that do not own the given application that they are connecting to an untrusted site.
In the future we hope to address the attack vectors described above and make attaching to an AM's web UI safer.