Intel, & to maybe a lessor extent AMD, made a run at the cell phone & low cost tablet & notebook markets -- Intel has since abandoned development of new hardware for these markets, & may push more powerful mobile chips downstream to help fill in future gaps in their product lines. Intel never managed a on-chip modem to compete with ARM chips, & that meant they couldn't compete in the market, so they pulled their resources to concentrate on future 5G cellular service, where they intend to lead. Low end Intel SOCs [System On a Chip] for those markets were re-purposed by Intel & other companies into small form factor PCs & PC sticks [think USB dongle with a PC inside]. The biggest advantages are at the low end of this market.
A part of the cost with a desktop or mini-ATX desktop PC is the case & power supply -- with a mini-PC [or NUC for Next Unit Computing as Intel calls them] the cost of the case is negligible, & the power supply is a much cheaper wall wart. Add a super cheap SOC & a mini motherboard to go with it, & no one can build a desktop PC for less. When you start upping the ante with a better SOC you get into laptop territory, & since they're made by the millions, you can buy a laptop for less on sale, & a laptop includes a keyboard & display. Up the ante further, with a mobile version of the i5 or i7, & you could actually save money with a full desktop PC using the more capable regular [vs. mobile] i5s & i7s.
So, what you've got commonly is a 6 in square by 2-3 inches tall PC that will play media files, run software & games that aren't particularly resource intensive, browse the web, do email etc., for generally $150 - $200, though you can do better than that, possibly by as much as $50 less, when one's on sale. While they're a niche market fewer people know about, they have been around long enough that some are in their 3rd generation. Mini-PCs are commonly sold complete or as bare-bones, meaning you have to supply your own RAM & hard drive, usually a smaller capacity SSD. The full versions may include Windows 10, while the bare-bones units are more likely not to include any OS.
Reliability &/or durability/longevity vary a lot by model, even with the same name brand like Intel on the label, so as possible it's best to get something that's been on the market a year or so, where you can look for reviews & such in case it has a habit of dying after a few or several months. Wi-Fi & Bluetooth is usually pretty bad, so plan accordingly. If you plan on playing video, using 2 sticks of memory [dual channel] makes a big difference. Finding compatible memory can be a huge problem with some brands & models of mini-PCs. Most mini-PCs use older generation SOCs that cannot support HDMI 2, so no 4k @ 60.
With a typical bare-bones unit you supply one or two sticks of laptop RAM which you insert after removing the case's cover, then shoehorn in a SSD -- it''s tight in there, so you have to be OK working in very tight, small spaces. Most mini-PCs have only a couple or a few USB ports, that may be USB 2 &/or 3 -- there are SOCs that cannot really support USB 3, though they're labeled USB 3.0, & even run USB 3.0 drivers -- so maybe consider a USB hub. Some have HDMI, while others have Displayport, mini-Displayport, or you might get some combo of 2 out of the 3. Watch out for restrictions, e.g. a displayport that can only be used with a VGA dongle or adapter. Also be aware that the bios will likely be very minimal, & may have some gotchas, e.g. the Beebox won't do anything without seeing a formatted hard drive or USB stick prior to installing Windows.
Myself, I bought a Beebox made by Asrock as an open box bare-bones unit for $116, using a store credit I had to bring the cost down below $100. I had 2 sticks of RAM, but it would recognize both at the same time, so I dumped ~$30 on a matched pair of 4GB sticks that I knew would work. The cheapest SSDs go for around $35 for 120GB, but I had an old 60GB SSD I used. I've got it running 10 pro, using a win7 key I had. I didn't want the potential hassle of Wi-Fi with 10, so I pulled the Wi-Fi + Bluetooth card, then added a $2 Bluetooth 2 USB dongle I had to a Logitech USB extension cable, which works fine. I have a cable card tuner, which lets me get encrypted channels like HBO, but it'll only work with Windows Media Center -- I got the Beebox rather than a $30 Android version because of that, running a hacked version of WMC in 10. SO far so good, & I can use it as a media player, or with an external drive, a Blu-ray player.