An application that “breaks” the connection between client and server. The proxy accepts certain types of traffic entering or leaving a network and processes it and forwards it. Note: This effectively closes the straight path between the internal and external networks making it more difficult for an attacker to obtain internal addresses and other details of the organization’s internal network. Proxy servers are available for common Internet services; for example, a hyper text transfer protocol (HTTP) proxy used for Web access, and a simple mail transfer protocol (SMTP) proxy used for e-mail.
Sources:
CNSSI 4009-2015 from NIST SP 800-44 Version 2

  An agent that acts on behalf of a requester to relay a message between a requester agent and a provider agent. The proxy appears to the provider agent Web service to be the requester.
Sources:
NIST SP 800-95 under Proxy from Web Services Glossary - W3C Working Group Note 11 February 2004

  An intermediary device or program that provides communication and other services between a client and server.
Sources:
NIST SP 800-113 under Proxy

  A proxy is an application that “breaks” the connection between client and server. The proxy accepts certain types of traffic entering or leaving a network, processes it, and forwards it. This effectively closes the straight path between the internal and external networks, making it more difficult for an attacker to obtain internal addresses and other details of the organization’s internal network. Proxy servers are available for common Internet services; for example, a Hypertext Transfer Protocol (HTTP) proxy used for Web access and a Simple Mail Transfer Protocol (SMTP) proxy used for e-mail.
Sources:
NIST SP 800-44 Version 2 under Proxy

  Software that receives a request from a client, then sends a request on the client’s behalf to the desired destination.
Sources:
NIST SP 800-86 under Proxy