Overview
Proxy server is an intermediary server between client and the internet. Proxy servers offers the following basic functionalities:

Firewall and network data filtering.

Network connection sharing

Data caching

Proxy servers allow to hide, conceal and make your network id anonymous by hiding your IP address.
Purpose of Proxy Servers
Following are the reasons to use proxy servers:

Monitoring and Filtering

Improving performance

Translation

Accessing services anonymously

Security

Monitoring and Filtering
Proxy servers allow us to do several kind of filtering such as:

Content Filtering

Filtering encrypted data

Bypass filters

Logging and eavesdropping

Improving performance
It fasten the service by process of retrieving content from the cache which was saved when previous request was made by the client.

Translation
It helps to customize the source site for local users by excluding source content or substituting source content with original local content. In this the traffic from the global users is routed to the source website through Translation proxy.

Accessing services anonymously
In this the destination server receives the request from the anonymzing proxy server and thus does not receive information about the end user.

Security
Since the proxy server hides the identity of the user hence it protects from spam and the hacker attacks.

Type of Proxies
Following table briefly describes the type of proxies:

Forward Proxies
In this the client requests its internal network server to forward to the internet.

There are some websites for sure that often publish free proxies. Why do they do that? I can not answer this question for sure but just try to guess. People can use free proxies in order to learn how to work with them. You can use free proxies if you do not care about anonymity. Anyway, I would not recommend using free proxies because it is too dangerous. This contact form will help you get safe german proxies for reasonable price.