Trying to figure out what technologies/frameworks a web app is built upon is an important part of application security, especially pen testing. It's something that should be done in the reconnaissance phase of an assessment. Knowing what an application is using under the covers is a definite advantage in your quest to pwn it.
Trouble is, it's not so easy anymore. There is a vast array of technologies that make up today's web application development landscape. Not only are there are different types of web servers, application servers, and programming languages, you also have to consider different development platforms (Java vs. .NET vs. something else), client-side JavaScript frameworks (Angular vs. React vs. something else), authentication protocols (OAuth vs. Kerberos vs. one-off vs. API token vs. something else), CMSs, CDNs, advertising networks, analytics engines, and so on. Is your head spinning yet?
For quick feedback on what technologies a web application is using, I recommend the Wappalyzer browser extension. It is available for both Chrome and Firefox. Once installed, you will see the following icon in your browser's toolbar:
Click this icon and you'll see a categorized listing of different types of technologies used by the website currently loaded in your browser. Here is an example:
I have personally found this extension to be very useful... for pen testing or even when you see an interesting-looking site. Find out what it's built on! This extension thankfully works with Firefox 55 and later, which is something that can't be said of many popular Firefox extensions nowadays (this is thanks to Mozilla's shift to use the cross-browser WebExtensions API.
One last important note about Wappalyzer - you probably want to uncheck the option (shown below) where you send them "anonymous" reports for research.