If you want to use an HP printer which is not a modern driverless IPP (AirPrint, Mopria, IPP Everywhere, Wi-Fi Direct Print, prints from smartphones) printer (then you do not need any Printer Application) then this is the right Printer Application for you.
It supports ~3000 different printer models, those supported by the HPLIP (https://developers.hp.com/hp-linux-imaging-and-printing/) driver suite from HP. These are mainly older inkjet and laser printers from the time before driverless IPP printers, but also the current models get continuously added by HP, even if they also do driverless IPP. You can still use this Printer Application then, but as a Printer Application is an emulation of a driverless IPP printer using the printer's own driverless IPP functionality is recommended.
If your HP printer is a PostScript printer you can alternatively use the PostScript Printer Application (https://snapcraft.io/ps-printer-app), for example if you have other non-HP PostScript printers and want to use only a single Printer Application.
Note that scanning will only get supported in later versions of this Printer Application.
HPLIP already ships for many years with most common Linux distributions (Ubuntu, Debian, Fedora, SUSE, ...) and has made many user's printers work and with this Printer Application these printers will continue to work in environments where only Printer Applications (and no classic printer driver packages) are supported.
Note: HPLIP is actively maintained by HP, they are continuously adding the newest printer models and adapting the software to new environments/Linux distributions. If all is going well they will sooner or later start providing a Printer Application by themselves. As that Printer Application will be native (not using classic CUPS drivers internally) and provide more functionality than this one (scanning, command line and GUI utilities, ...) and always up-to-date with HP's newest printers and scanners, this Printer Application will get deprecated then end eventually removed from the Snap Store. Please switch to HP's Printer Application in that case.
This Printer Application emulates a driverless IPP network printer (IPP Everywhere) for each physical printer set up with it, so your computer's printing environment discovers it automatically and makes your printer(s) available for printing. Like on a physical network printer there is a web interface for administration, here especially also for adding and configuring printers. You find it with your browser under https://localhost:8000/. Note that currently printers have to get added via the web interface to use them. In the future, there will be utilities to easily find non-driverless printers and find the correct Printer Application for them.
When adding printers via the "Add Printer" page of the web interface, they are usually auto-discovered and listed in the "Devices" drop-down list, often more than once. The versions marked with "HPLIP" use a special communication protocol so that you can print and scan simultaneously on a multi-function device whereas the other entries allow bi-directional communication with your printer, which especially allows querying PostScript printers for default settings and for their configuration of optional accessories (extra tray, duplex unit, finishers, ...). So choose the more suitable for your use case.
With modern printers usually being driverless IPP printers, classic printer drivers, installed under CUPS by its web interface or a printer setup tool, are deprecated and replaced by Printer Applications (for the non-driverless legacy and specialty printers) which emulate driverless IPP printers as this one.