The main purpose of using a proxy, VPN or anonymity service is to hide your identity and location. A leak in this context is any information that could be traced back to your true identity. Most users are concerned about leaking their true IP address, but other information such as your location, browser and operating system can also be used to detect a user who is trying to hide their identity.
Any website or service with an interest in your real identity or location will be interested in what you’re leaking. Netflix and YouTube want to stop people getting around their geoblocking. Leak detection can be used to prevent all sorts of nefarious activities from blog comment spam to credit card fraud. And lots of people are very keen to find who exactly is seeding those torrents so generously.
Whilst green lights for every test shows a relatively private system, there’s simply no way to ensure you’re completely secure. We test a lot of the known leak factors, but not all of them, and our tests could be inaccurate or buggy. If your VPN dies while you’re using it, your connections could also be rerouted.
Port scanning of your IP address would also reveal more information about your situation. We cannot perform those scans as your ISP would send us angry messages. But a malicious website won't be so sensitive about upsetting ISPs like we are.
Finally, unknown exploits are always a hidden danger and new ones are always being discovered.