First of all a proxy is an application or system which services the requests of clients by forwarding the requests to other servers. SOCKS is an internet protocol which allows for the transparent proxying of applications. The SOCKS protocol was developed at MIPS in the early 1990's and became public in 1992 when SGI purchased MIPS Computer Systems. RFC's for SOCKS v4 (NEC) and v5 followed.
SOCKS4 provided for connections to arbitrary TCP services and operates on layer 5 (SESSION) of the OSI model. This places it below the Presentation (ex. SSL) and Application (ex. HTTP) layers which is what makes it transparent to application protocols. Many alternative proxy methods at the time required application changes which becomes more difficult to support as new applications and protocols are developed. SOCKS4 supports TCP connections only and optionally simple authorization using a userid. SOCKS4a added support for sending proxy requests before resolving the domain name of the target. SOCKS5 (RFC1928) built on SOCKS4/4a and added support for UDP proxy connections, authentication methods, and Ipv6. In a standard SOCKS connection a client connects to a SOCKS proxy server and makes a CONNECT request which specifies the destination IP (or domain name) and port it would like the server to connect to on its behalf.
In typical proxybot infections we investigate proxy servers are installed on compromised machines on random high ports (above 1024) and the miscreants track their active proxies by making them "call home" and advertise their availability, IP address, and port(s) their proxies are listening on. These aggregated proxy lists are then used in-house, leased, or sold to other criminals. Proxies are used for a variety of purposes by a wide variety of people (some who don't realize they are using compromised machines), but spam (either SMTP-based or WEB-based) is definitely the top application. The proxy "user" will configure their application to point at lists of IP:Port combinations of proxybots which have called home. This results in a TCP connection from the "outside" to a proxybot on the "inside" and a subsequent TCP (or UDP) connection to the target destination (typically a mail server on the "outside"). How reverse-connect proxies differ will be highlighted in the next section.