Seamonkey is a web browser and application suite based on the ancient Netscape Communicator from 1997. That suite was continued as the Mozilla Application Suite which was later renamed to Seamonkey.
Features and usability
Seamonkey is an application suite with a mail client and a web composer feature in addition to the web browser part.
Seamonkey's development has essentially stood still for over a decade, and it shows. The browser back-end is updated with new versions of the Gecko rendering engine Firefox uses - with a lag. The web browser part is mostly fine. The rest of the application suite shows clear signs of decades of abandonment. The e-mail client and composer were never that great to begin with and no improvement over nearly two decades does not help.
Seamonkey used to support the same extensions as Firefox. Then Firefox went ahead and deprecated all the good extensions for that browser and required all new extensions to use a new API. Seamonkey is unable to use these new extensions. This means that only older (outdated) no longer updated Firefox extensions can be used by Seamonkey. But among those are some nice gems available to seamonkey, but not for a current firefox.
There simply isn't much of a use-case for this browser. Firefox would be a better choice if you want a Gecko-based browser.
The remaining use cases are:
1. You have a real nice Add-On which does not work in firefox anymore. Only in Seamonkey does it work.
2. You are a Luddite and hate to update stuff every 2 hours, wrecking your whole installation in the process and constantly changing the workflow in a highly disruptive manner. And then change it back again. And so forth.
3. Waterfox is also aiming at backwards compatibility, as an alternative to seamonkey.