Companies require varying levels of control over their server infrastructure, which is why providers offer these two choices to their clients.
A managed dedicated server is one that is constantly maintained by the provider in ways such as: component replacement, security monitoring, software updates etc. This allows the company using this model to save time on infrastructure management and spend its time on more long-term goals while the provider takes care of the basics.
Unmanaged servers are ones that are fully controlled by the client in all aspects; the only responsibility of the provider is to maintain the environment for the infrastructure to function. This option is often utilized by companies with their own approach to server management, allowing for more immediate control.