
In-band can be rendered unintelligible by high-compression codecs or poor quality connections, whereas out-of-band requires the far-end gateway to detect and act on the received packets. When talking about VoIP, in-band DTMF means that the tones are sent in the audio stream in the traditional way, whereas out-of-band DTMF is sent as specially formatted data packets. Especially useful if internet is down or your other means of connecting to the machines is not working and you need to get to your iLO or iDRAC to start a server or the like.

Usually an out of band DTMF, in my experience, is a dial in access on POTS to a data center to access a terminal that can control or monitor functions of the data center.
