Use proxy servers defines if a proxy is being used. Otherwise Atomic Lead Extractor will request the pages from the sites directly without a proxy use. If you use proxies you need to set them up with specified address, port number and authentication info. The default and recommended value is to uncheck "Use proxy servers". However, if you check the box, you'll be able to add, remove, paste, import, save the proxy list.
Process every link of domain via separate proxy server - if you have this option checked, search will be handled by various proxies. You just need to set them up.