I currently have my trees parented the same as at 10:09, however, When I hide the parent tree it only hides the branches (not trunk or leaves), however near the end of the video I see the instructor click hide on the parent and toggles the entire tree.
Am I missing something? 
I *think* you need to right click on the parent and 'select hierarchy' then click hide and everything will be hidden
So when I do that it highlights parent light blue, and dark blue highlights leaves and Tree_C_Trunk, then I click hide on the parent and it still hides only branches.
Not sure if that's the intended functionality. I'm too inexperienced to know. lol
I don't know what he did, but you can use shift+ [ or ] to add Parent or Child to selection and then press H.
Is something about my hierarchy incorrect? I guess my concern is if my hierarchy is incorrect I will run into issues with this later in the course, or if I am just putting too much focus on something small.
@BirdOfWar If you click the trunk and move it around and everything moves with it you have your parenting hierarchy good.
Need more info. You need to explain step by step with images, name your layers more precisely and referring to the specific objects you're trying to hide etc. (or just make a video with commentary) exactly what the problem is cos basically all you're saying is
'it doesn't work - why?'
without more information it's impossible to answer
If you have three objects, the trunk, the branches and the leafs, in order to hide an object (with H on the keyboard) you need to have said object selected. So if you select the trunk and press H, the trunk will be hidden but the other two objects will remain in view. If you want to hide all three objects you need to have all three of them selected. You can also toggle the eye icon in the Outliner for each object. Alternatively, you can put all three objects in a collection and just hide the collection for all the objects in it to go away.
thehomme Sorry for the lack of information, I was hoping what I included was sufficient.
Okay all really good answers from everyone. Thank you all for the feedback.