O boy.
A vinyl is short for a vinyl record. They are plastic-like rigid discs about a foot in diameter played on record players. A needle runs along grooves in the record and vibrates. These vibrations are amplified and sent on to a playing medium, like speakers.
Many Dj's use vinyl because of its scratchability, and full sound. Many use CD's instead because they are cheaper, more available, and more transportable.
I personally liuke vinyl, and would reccomend it to most people.