This is a pretty uninviting term to many, especially the non-gurus, but in most cases is not as 'non-servicing' as it seems. In fact, I think someone one day soon, ( who knows maybe me ) will coin a new phrase to replace the term 'unmanaged' - similar to how 'used cars' is now 'pre-owned' or how 'apartment complexes' are now 'rental communities'. The truth is that unless you just picked a lousy provider or have unreasonable expectations, unmanaged hosting offers more service and support than most think.
While exact definitions vary among providers, generally speaking managed hosting means your provider takes complete or near complete care of your server. This can include anything from basic system maintenance and patches to applications maintenance, security, monitoring, etc. Someone that needs dedicated hosting and wants to rely on their host for pretty much anything and everything regarding their server needs to strike a relationship with a managed service provider. Full blown managed services involve lots of skilled people hours. Not only that, since every managed customer is unique, it's hard for a managed provider to be overly systematic. For this - expect to pay a great deal more than today's budget server provider but if your needs demand it, and you choose a solid provider it should be money well spent.
Unmanaged dedicated hosting obviously refers to dedicated servers with less, little or none of the skilled people support you'd expect to find in managed. You signup, you pay, and in a few minutes to a few hours you get a welcome email with IP address, login, FAQ's, etc. - Beyond that you are pretty much on your own. Relax - you are not really as own your own as it seems.
First off, most unmanaged providers do in fact offer technical support, and most that we've seen is very good. If you choose unmanaged dedicated service you do need to have someone on your team that knows the technical side a good bit, but they don't necessarily have to be experts. While you may have to wait 12 - 24 hours or you may even have to pay extra for it, nearly all the unmanaged providers I know do have high level techs available to handle serious issues. In addition most providers give some sort of immediate reboot service. Unless you've been tinkering with some critical config files or have a hardware failure, a reboot can help with a range of issues. Lastly, unmanaged providers may not support you or whatever you put on your server after you move in, but they do stand by the hardware and software they sell you. If a hard drive crashes they are going to replace it for you (although you had better be doing your backups) and if your system crashes most will fix it for you.