Shell out and use normal commands, such as :!mkdir my_dir and :!touch foo.txt (as mentioned in Jake's answer here) will create the directory and file in CURRENT working directory, which is the directory when you started your current vim process in the beginning, but NOT NECESSARILY the same directory of the file that you are currently editing, or the same directory that your :Explore explorer is currently viewing. When in doubt, always use :!pwd to check your current working directory first, and use relative path when necessary.
So if your project contains multiple sub-directories, a more convenient way is to:
type :Explore to enter the explorer mode first,
and then you can easily navigate to whatever sub-directory you like, by typing up-arrow or down-arrow (or j or k) to move cursor, typing Enter to enter a sub-directory, typing - to go up a level of directory. (Note that, all these navigation does NOT change your current working directory either);
Now you can type d to be prompted for a directory name, or type % to be prompted for a file name, and then they will be created in the directory currently shown on screen.
PS: These keys are actually mentioned in the built-in help F1.