Hello Miguel
In-band device management means that you connect to the management interface of a device (using Telnet, or SSH for example), via the network infrastructure as well as the device interface that is also used for user data traffic.
Out-of-band device management means that you use an alternate path, different from the one used by the user data traffic, to gain access to the management interface of the device.
You can understand the difference even more clearly when you think about it this way: If your network fails, user traffic will also fail, and so will in-band management. But out-of-band management should still be available because it uses a completely independent path to connect, a path that is unlikely to be affected by any failure to the infrastructure used by user traffic.
Options for out-of-band management include the use of a PSTN phone line connected to a modem which in turn is connected to the console port, or via an independent internet connection over cellular or xDSL, or cable. Many Cisco devices have an ethernet port labeled “management” which is used for this very purpose.
I hope this has been helpful!
Laz