I ran into similar confusion. I wasn't even sure how to properly setup the user so that I could send a push notification directly to them. Then I found the following post:
Channels and Targeted Push Notifications
Note the last item under the Channels heading:
Most apps might find it useful to have a channel for each user so that
they can send messages to a user across all their devices and have
users follow others in the app.
So, now I know that I should subscribe each user to a channel that uniquely identifies the user (e.g., the 'bobsmith@foo.org' channel).
After I have subscribed the user to their channel, I can call Parse's REST API via my ASP.NET application. See Sending Pushes in the Parse REST API Developers Guide.
For an ASP.NET/C# example of how to submit a push notification check out this answer.