A Managed Services Provider (MSP) is a company that lets you delegate specific IT operations to them. The MSP is then responsible for monitoring, managing and/or problem resolution for your IT systems and functions as well as automate the mundane tasks that users can and should do, but often overlook. This can include virus updates, software updates and patches, backups, monitoring and inventory auditing and control.
Basic services often start with a monitoring service which notifies you of problems, but you have to resolve them on your own. More intensive services cover everything from alerts through problem resolution.