A managed switch allows you to control the individual ports of your switch. Features of course vary with manufacturers and models, but even the most basic will have the ability to turn the port on or off and control its link speed and duplex settings. That control is for security; it prevents someone just walking in and connecting to your lan through an unused port.
Beyond that, you might be able to specify a particular MAC address that is allowed to connect. That prevents someone from replacing machines with their own. You might be able to set login authentication, also. You may be able to designate certain ports as "high priority"; for example the ports your servers are on. Setting bandwidth limits, monitoring port traffic and of course logging are also features.
VLANS (Virtual LANS) are a popular option. This allows you to set a broadcast domain on certain ports, so that broadcast traffic isn't passed on to the other ports. This can also isolate machines from each other for security purposes.
Link aggregation ties together multiple ports, allowing two switches to be connected more than once for higher throughput between them. The switch may support Spanning Tree, which lets you have multiple paths for redundancy without having to worry about looping.
These switches may also have snmp agents that will report status to snmp monitors. Nowadays they usually have a web interface for configuration in addition to the traditional command line method. Older models might require access through a serial console, but more recent devices will have the web interface.
