A proxy is an intermediary system that traffic flows through. Can you provide more detail on what you're looking for?
Common port states would be
Open - the port is wide open and something is listening on it
Filtered - there is a firewall or other filter filtering that traffic
Closed - nothing is listening on that port
Nmap can be configured to use different techniques and analyze responses. Systems will respond in predefined ways that allow tools like nmap to determine the state.
A proxy server is a computer that acts as a go-between for the user and the target server. The client connects to the proxy server first, then requests the resource from another server. Consider an email or an HTML page. The proxy then connects to the specified server and retrieves the resource, or returns it from its own cache. Proxy servers are used by businesses for security, network performance, and access to "remote" resources. Choosing a proxy from an off-the-shelf source like this soax.com is usually easier. Proxies are used by individuals to anonymize traffic and circumvent access limitations.