The trademarked name for Commodore's line of cassette drives for its early computers and consoles. The name is quite obviously a collision of "Data" and "Cassette".
The Datassette was the accepted form of personal data storage on most of the Commodore line for quite some time due to the cost of floppy disk drives]. There were the external models 1530 and 1531, released in 1983 and 1984 respectively, as well as the early Commodore PET which had a built-in in Datassette.
The Datassette was essentially just a cassette tape player with a special output system that sent the signals on the tape in a differential serial signal over a serial connection to send the data to the host computer (at least, on the 1531 it is, I'm not sure about the 1530). The used standard-issue audio cassette tapes, though I'm not sure of the actual data density for tape. Playing a cassette tape with data stored on it would not be a pleasant experience, either sounding like loud, sharp square waves or simply disjointed white noise.