At the simplest level a managed switch allows you to control each of the ports. Turn them on and off, set the speed and duplex, setup VLANS,do QOS, do trunking and use SNMP to monitor its status. There are also Level2 and Level3 switches, the difference being how deep into the "packet" it looks before it decides what to do.
Also bear in mind that even with unmanaged switches there is a huge difference in how "powerful" the switches are. By that I mean how much bandwidth can they really handle (backplane).
With some of the highest level managed switches the line starts to blut between a router and a switch.
"Arms discourage and keep the invader and plunderer in awe, and preserve order in the world as well as property... Horrid mischief would ensue were the law-abiding deprived of the use of them." - Thomas Paine