An internet service provider assigns an IP address to every connected user, and any website that user visits can log it. A proxy server sits between the user and the destination site, forwarding requests on the user's behalf so the site sees the proxy's IP address rather than the user's own, which is the mechanism behind most IP-masking and geo-location-bypassing tools.
For SEO work specifically, proxies show up most often in tools that check how a page looks from different locations, useful for verifying that geo-targeted content, hreflang tags, or local search results are actually behaving the way they're supposed to for visitors in a given country. They're also used, more questionably, to run large-scale automated checks (rank tracking, scraping competitor sites) at a volume that would otherwise get a single IP address rate-limited or blocked. On the flip side, a proxy or VPN complicates diagnosing a real user's experience, since testing a page from behind a proxy doesn't necessarily reflect what an ordinary visitor's browser and network actually see.
