Depending on the aspect ratio of the video.

If you are putting the player in a 4: 3 ex: 640x480 format and the video is in that format, there will be no border. Now if your player is 16: 9 (720p) and your 4: 3 video as in the case of your photo will have border.

(To be exact, this player should be 21: 9 and your 16: 9 video, both widescreen but with different proportions)

To understand screen formats: Wikipedia: link

Solutions:

Will you always have a video standard? if yes, then place the player with the exact dimensions. In case the height you want.

<iframe width="640" height="480" src="//www.youtube.com/embed/Ipsi5aJzXBc" frameborder="0" allowfullscreen></iframe>

 width="640"  //largura
 height="480"  //altura

This border in some videos is the problem of editing itself, so it is impossible to solve the problem by scaling the player, if you size the player by width and height , it may harm others.