The proxy funnels our web inquiry thru the server that the proxy uses, so it doesn't look like it came from your computer.
This has practical uses. Keyword research and scraping creates a lot of Google queries. By using proxies, these inquires do not come from the same IP address, and they do not get temp banned.
When creating backlinks, a proxy helps it look like you, the site owner, did not leave the link because it did not come from your IP address.
If you were to visit a site, say one that you were not a member of, and somehow you had found the link for a download (ahem), but had not really joined the site or purchased a product, and you visit the site, your IP address will not be logged, your proxy IP address will. It will look like you never visited, because the server logs will record the proxy IP address.