Konqueror is a web browser and file manager, developed by KDE and included with most KDE metapackages in Debian. Formerly one of the most important packages in the KDE Software Compilation, it now sees sluggish development, though it's still highly functional and contains a large amount of functionality that no other single application can replace. It has also been ported to all KF5 libraries, keeping it well-integrated with modern systems.
Konqueror uses the Dolphin KPart for its file management, and as such, it mostly behaves as an embedded version of Dolphin, and it follows Dolphin's settings as well. With konq-plugins installed, you can configure these straight from Konqueror's own configuration.
One reason to use this instead of Dolphin is better integration with the files you open. Different KParts are used in Konqueror to allow you to instantly view and display images, text files, archives, etc. that you open through Konqueror without needing to use any external software. This keeps your workflow in one place.
As of recent versions, Konqueror now uses Qt WebEngine by default. This gives great coverage of recent web standards and keeps it compatible with virtually every modern website. Even technologies such as WebGL and WebRTC should work out-of-the-box.
The browser still isn't fully integrated with WebEngine though, and some extensions like AdBlock that are added by konq-plugins won't work properly yet. KHTML is available as a fallback, though be warned that it's extremely sluggish and does not support any recent web standards.
You may find Falkon useful as a more modern web browser from the KDE project.
https://docs.kde.org/trunk5/en/applications/konqueror/index.html - The Konqueror Handbook