Unmanaged dedicated server hosting means the provider will only setup your server with OS and you will have to manage the rest. You will not be eligible to get after sale support.
When you are purchasing a dedicated server, you must be looking to host your mission-critical application. So, instead of taking a risk of Unmanaged, you should go with semi-managed or managed service. If you are tech savvy and do not need any assistance then you can go with unmanaged service.
I strongly recommend AccuWebHosting for their superior hardwares and super speedy support. Even if you have a Self Manged Server with them, they will provide you maximum possible assistance for your technical issues.
Basically, with an unmanaged server the provider is not going to help you at all with your server, they will just handle installing the operating system for the first time and the hardware.
If we are talking about the fully managed server, it usually means the provider is going to take care of everything for you, like - setup, installing software, migrating accounts, any requests you make from them, etc.
Unmanaged servers, on the other hand, leave the work of keeping your dedicated server maintained up to you, for the most part. There are some basic tasks that will be done for you, but you will be the one who needs to install security updates, patches, and manage other aspects of the server itself.