Hmmmm.....2 things spring to mind...
A. This tutorial isn't the best. It mixes Illustrator with Photoshop with very little definition between the two and to be honest is like using a sledgehammer to crack a nut.
B. Even if this tutorial was written so it could be understood its a fairly advanced tutorial for someone not familiar with Photoshop...or any other Adobe product for that matter.
I say that purely as this is posted in the 'Newbies' section.
Are you following this for experience or because you really want to crack a nut?
If its for experience then I suggest you forget this one and move on....there are many, many GOOD tutorial sites out there that wont have you jumping through hoops for something simple.
Here are just two really good Youtube channels:
BlueLighteningTV:
https://www.youtube.com/user/bluelightningtv
Phlearn:
https://www.youtube.com/user/PhlearnLLC
Either way, you'd be much better off using your time to learn the basics of Photoshop rather than wasting your time trying to follow this, [or any written], tutorial...which, when all said and done, will only teach how you how to do one specific thing.
Its a good site, but its not known for it tutorials.
If you want to persevere with it though, 'cutting out' is not a PS term but I think they mean 'remove everything that doesn't look like land'....cut out the bits you want to keep. This is where knowing the basics of PS would be beneficial...you'd know exactly how to do that and it wouldn't be holding you back. That's not to say its the right thing to do but at least knowing the basics you could make your mind up as to its validity.
Regards.
MrToM.