Similar to dedicate server hosting, managed hosting service is on a per server rental basis type of hosting too, but slightly differ from general dedicated hosting services by offering partial to full server support to the client. Extra support services like attending to your server software issues for you, monitor your server services to keep them available at all times and attend to any server problems on your behalf are available in managed hosting service.
Basically, managed hosting provider will be monitoring your server for you like a normal technical personnel you have hired to maintain your server, this level of support is generally not available in lower end dedicated server hosting service.
Hosting fee is higher than dedicated hosting and co-location hosting as major portion of the hosting fee goes to the higher level of support provided. There is a note to be taken, be sure to check thoroughly the support level provided of your short-listed web host, there are partial managed hosting and full managed hosting service, which means certain web host offering partial managed hosting may have listed certain type of support requests to be extra chargeable on top of the hosting fee.