Anonymous proxies mask your IP, replacing it with an IP that can make it appear to the server you are visiting, or to anyone monitoring Internet traffic, that your computer is now in another location, even another country.
Any server you visit can detect your real IP unless you use a proxy. Preferably with a very high anonymity rating like a High-Anonymous proxy. In practice though it is highly unlikely any server will noticed you are using a proxy unless the company or institution puts some effort, and money, into it by adding a bit of code that can detect the real IP.
If your goal is to protect your privacy and do not want the servers you are visiting to know your IP, or even that you are using a proxy, then you will need a High-Anonymous proxy, or better.