Hi OP,
I'm also getting into more serious photography/ videography - Nikon D3100 here. Also quite young, <18. Woop.
Okay, this is basically what I think you want to know:
Depth of Field/ what I call "bokeh" is entirely controlled by your f-stop/ aperture. I'm trying to include multiple terms because if you want to google to expand your knowledge, which I think you should be doing if you are serious, some sites will only use one term.
So, f-stop/ aperture is how much light you're letting into the camera. This is how the two words differ. A low f-stop (e.g. f1.8) means that the hole letting light in is really big. This is also called a big aperture. Meanwhile, a high f-stop means a smaller hole, and hence smaller aperture.
okay. So f-stop is vital to getting nice bokeh, which nearly everyone on here has pointed out. The difference between your 50mm lens and JacksGap's (the twins' youtube channel is called that) 30mm lens is the focal length. Obviously.
Now the bigger your focal length, the more "zoom" you have into an environment. Hence, JacksGap's camera can probably be placed closer to his face than you can with yours. This is really important for bokeh.
The closer an object is to the camera (given that the camera is focused to that said object), the better the bokeh in the background will be. Conversely, the further away the focused object is from the camera, the less bokeh the background will have.
Just learn to take lots of photos/ videos. It'll all turn out.
Another thing, I think the difference between the first and second video is this. In the second video, the camera may not have been exactly focused in that perfect position. Also, first video may have been shot in better quality than the second. i.e. 1080p vs. 720p.
But really, just have fun getting into photography and videography. You'll understand the camera a lot better with experience rather than just reading all of these replies.