No technical mechanism is used to distinguish an anonymous proxy from a "high" anonymous proxy (sometimes called an "elite" proxy). The only difference is that the latter is not found on common blacklists such as the DNSBL. This is typically done by giving a unique IP address to each person, so spammers will not be using the same IP as you and getting it on a blacklist.
Non-anonymous proxy - Sometimes incorrectly called a transparent proxy, a non-anonymous proxy is one that transmits your IP address in
X-Forwarded-For. These proxies are not usually on blacklists because your original IP address is known to any site you are connecting to, allowing them to blacklist based on this forwarded IP. These proxies forward your IP address specifically to allow destination sites to block any given proxy user's IP address, rather than the entire IP. This lets the proxy serve its primary function (e.g. caching).
Anonymous proxy - These proxies simply do not forward your IP address. They are usually abused by spammers, and because the destination server cannot distinguish a legitimate user from a spammer, it is forced to block the entire proxy, usually through public blacklists.
High anonymous proxy - These proxies are the same as anonymous proxies, but are not found on blacklists. This is usually accomplished by giving each person a different IP address or by retiring an IP address and using a new one as soon as it becomes listed on any popular IP blacklist. These proxies may or may not reveal that they are proxies via rDNS lookups.
Be aware that high anonymous proxies are designed only to prevent the IP address from being put on blacklists to make navigating the web less of a pain, not to hide the fact that you are using a proxy from anyone who actually wants to find out. There are countless ways to determine the fact that you are using a proxy which cannot be avoided. Furthermore, neither honest proxies, nor commercial VPNs provide particularly good anonymity due to traffic analysis attacks, among other things. Using a network such as Tor designed from the ground up for anonymity is required for strong anonymity, though they make no attempt to hide that you are using it from the destination.