A proxy is essentially an IP address that works in conjunction with your home IP. Proxies are used to mask your IP address and protect anonymity. Proxies are pretty much a necessity to prevent your IP from being banned on any of the sites that Phantom supports.
Proxy speed is pretty necessary for most support sites. To have the fastest speeds, either your home wifi network must be fast or you must have a good server that is near or at the same location as your proxies. (See "What is a server?" for details on servers).