What is meant by an application gateway?

It is the least specific gateway term. Sometimes it means a gateway specialised in one particular application and its protocols; often it is just another name for one of the other gateway types, multi-function gateways included.

One example is Microsoft's Azure Application Gateway, which combines load balancing for web applications, SSL termination, a web application firewall and several other functions. When the term appears in a design, ask which functions are actually meant before assuming any security control.

Go deeper:

• Microsoft Learn — What is Azure Application Gateway? — the multi-function example: load balancing, TLS termination, WAF.
• Application-level gateway — Wikipedia — the narrower, protocol-specific meaning of the term.