Now, even though you managed to pause your previous video, that doesn't mean your web browser won't stop downloading the content of that video to your HDD which is called video-buffering. Now what happens is, if you have a moderately faster internet connection which can barely handle a single video, but now two videos are using your connection's bandwidth.
So, most probably, unlike watching a singe video without any distractions (you know those inevitable "pauses") when trying to handle two videos at the same time, you'll be having difficulties while watching the second video.
The point is, just because you "Pause" it, doesn't mean the actual connection or the data exchange between your PC and YouTube (in this example) is terminated.
Now you basically have two options.
1. Close the tab of the previous video, which will solve your problem or...
2. You can manually stop the data-exchange/buffering thus you can still keep that YouTube video open, yet it won't use your bandwidth.
The easiest thing to do is to just close the tab, but what if you were in a web page that contains more than one flash video. After pausing the first video (before it reaches the end), if you play the next one, now you simply can't use the "method - 1" to get rid of the first video using your bandwidth. In that instance, manually stopping the video buffering/downloading will most definitely come in handy!.
How can I do that?
Simple, just right click on the video that you want to stop messing around with your internet bandwidth :P and from the menu choose "Stop download". That's it!, have a look at the below screenshot to get a better understanding.
|From the menu choose: Stop download (selected in blue in the picture)|