Can someone explain 'buffering' and 'initializing'?

Today, I went on MTV to watch the details 'From G' to Gents', a reality show. I clicked on the screen and waited for the show to pop up. I watched for 20 minutes as the video began to play and then quickly shut down indicating "buffering" and then "initializing". The video would start up again and then shut down over and over. This happened for 30 minutes! For some reason, I am unable to watch some videos from my home computer and/or work and I don't understand why? I would love someone to explain how this process works. Why is it that some videos jump right up and continue until the show is over, and others either won't play at all, stop in the middle and continue to restart, or get almost to the end, and cut off before the show is over? Is there something I can do? My computer at work runs much faster than mine at home so I expected the one at home to be slower. Thank you for your knowledge.