It's because you took the video with the phone turned in portrait position. Take it again in landscape. Unless this is the effect that you want, don't take video with the phone turned upright.
However, if you really want the video in portrait, if possible, try changing the video settings and the output to 9:16 instead of 16:9. The problem will be that most video containers, especially for web design expect video to be in landscape mode and you may still be stuck with the black bars.
If you are anywhere near me, you won't be able to redo the video because you'll lose your golf balls in the snow.
browj2...thanks for the quick reply. so my source is the issue. I want be able to re-record anytime soon, so I'll need to try and switch to 9:16 "somehow".
Do a test recording with your iPhone turned sideways so that it takes video in the normal way, landscape, 16:9. Import it into FastCut and it will properly fill the screen, same when you export.
I don't have FastCut so I don't know what the possibilities for changing the parameters are, so I don't know if they can be changed to 9:16. Again, I wouldn't recommend it. I found that most viewer programs do not like videos that do not have standard parameters; they accept 4:3 and 16:9, but give errors if something else is used.
If you really want an indepth discussion on this, read through this thread. Look at the oldest replies first.
I'm curious to know how you wanted the published result to look? How could it be displayed any other way than that on your web page, which looks fine to me? It has to accommodate not only your own text during the movie but also the YouTube tools, and it also has to fit into the space above your long list of other activities.
Or did you really intend to show a full (normal) landscape of the course, instead of focusing exclusively on the player? The fact that you (instinctively?) rotated the camera implies not.
@John CB: Black balls! Husky over to the patent office when the drifts clear. I'll accept a token 10% of royalties...