Advanced-checker.com falls into the category of hoax websites targeting iPhone users. Typically, pages of this type attempt to scare their visitors into installing a promoted application by claiming that the user's device is simply infested with numerous malware threats. Massive damage has already been caused to the device apparently and, if the promoted application is not installed immediately, the non-existent threats will cause even bigger problems.
Advanced-checker.com doesn't go that far into the fearmongering territory but the claims it makes are equally as false. The site displays a pop-up stating the iPhone needs a clean-up to its supposed slow performance and the rapid discharge of the battery. Infosec researchers have observed two different variants of the messages displayed by the site but both ultimately try to convince the user to install a PUP that will supposedly clean the device.
Users should never trust the messages displayed by such shady websites. Even if the promoted application is legitimate, you should still get it from the official application store and not through an unfamiliar website that you randomly landed on during your browsing.