An unmanaged server is defined as one which the data center sets up the hardware, connect it to the internet, assigns the IPs and install the OS and maybe the control panel and the rest is up to you. Your tasks would be to configure the server, install programs, add your firewall and troubleshoot.
A managed server would come with the above plus probably some sort of server monitoring, troubleshooting services or some hardening services. There are different degrees of managed service so you need to check with the data-center as to what is included and what is not. Some may go to the extend to helping you install program, set up firewall, add sites to your server and so on.
Generally servers are offered as unmanaged unless they specify it is managed.
So if you are good at server management then an unmanaged server would be good for you but if you need some hand-holding especially if it is your first server, you might want to get a managed server, select one which meets your requirements.