Records are made from vinyl (PVC) and have sound recorded in grooves at specific speeds - the playback rotational speed being measured in RPM, or revolutions per minute. Records are manufactured by pressing, and whilst a more expensive medium than CDs or MP3s, they are still used for a lot of music because of the ability to directly manipulate the music. Turntablists use vinyl for scratching, and many djs mix only vinyl because it is easier to move around the audio.
Records come in speeds of 33rpm and 45rpm these days, but previously in history records have been manufactured for speeds of 16rpm and 78rpm. Some modern turntables do come with a 78rpm playback feature, for example the Stanton range of turntables.