I would want to explain this more in details and more technical.
1) Transperent proxy:
It just forwards you request, acts just like a gateway. The problem is that the host you are accessing via this type of proxy lets the host know that you are using proxy. This is because the HTTP response show sensitive information about you. X-FORWARDED-FOR especially.
2) Anonymous proxy:
This proxies doesnot send X-FORWARDED-FOR, so it improves privacy.
3) Elite proxy:
This also strips HTTP_VIA and HTTP_PROXY_CONNECTION, that makes the host you are trying to reach "no way" to know you are using proxy.
It is all about how the proxy server handles http. No dark magic. I hope that I was useful.
Regardz.