The black bars — better known as letterboxing (black bars top and bottom) or pillarboxing (black bars left and right) — are a typically result of your player not being the correct size for your video content.
If you're copying the embed code from the video page on your account, then just make sure you tick the 'Lock aspect ratio' checkbox before changing the width/height of the player.
If you're manually coding the embed codes, then you need to take the player type (Full, Simple, or Mini) in to consideration. The Mini player overlays the timeline, so the player is exactly the same dimensions as the video. However, the Full player and Simple player are taller (42px and 21px taller, respectively) than the video to account for the timeline/controls below the video.
Furthermore, if the instructions above don't remedy your black bars, then it's likely they are part of the video file. Always make sure you're using the same aspect ratio when editing your videos. Mixing 16:9, 4:3, and/or 3:2 video and image content can result in black areas within the video. You should scale up content smaller than the video's aspect ratio in order to eliminate those black areas.