It clearly shines at basic REST requests,

Postman is perfect for testing various HTTP requests with its quick and deep ability for manipulating the headers and payload. This makes it ideal for testing and debugging APIs and even simple web applications. Postman offers various payload types (raw text, JSON, form-data, etc.) and customizable HTTP headers. Requests are sorted into tabs, saved in collections, and recorded into a history -- all of which are helpful, but which can also quickly grow unwieldy if one isn't careful.

Postman is flexible enough that you can even use it for less typical requests (i.e. SOAP), but it clearly shines at basic REST requests and offers enough fine tuning to see what's happening "under the hood" of an HTTP exchange. (For instance, when authorization headers were being lost in a recent project, Postman allowed me to disable automatic following of 301 redirects, revealing an invisible but important step in the request.)

There is a wealth of advanced tools which I haven't even begun to explore, but individuals on other teams have used it for more automated situations. The vast majority of its users in our organization are using just the basics for simple requests.