VLC was the client for the VideoLAN project, with VLC standing for VideoLan Client. Originally developed by students at the École Centrale Paris, it is now developed by contributors worldwide and is coordinated by the VideoLAN non-profit organization.
One day, people from the Ecole Centrale's Networking Students' Association VIA (VIA has many clubs, amongst those is VideoLAN.) came back drunk with a cone. They then began a cone collection. Some time later, the VideoLAN project began and they decided to use the cone as their logo.