Did you read the article? It explains the whole thing.
Aliases point to Mapped Objects. So, Aliases.MyApp.MyForm.EditBox points to the mapped object... and the mapped object is used then for finding and identifying the object. Aliases are, exactly as the name implies, an "alias" for the mapped object.
The idea is that MySubPanel and AnotherSubPanel are mapped to be able to provide identification... however, because they are not strictly needed to be referenced for the test itself, the Alias edit window allows you to "collapse" the tree to be able to make referencing objects more user-friendly.
This is more easily seen in Web applications where a single text edit box may have a full path of something like
NameMapping.Sys.Browser.MyPage.Form1.Panel1.Table0.Cell13.Panel2.Table1.Cell23.TextBox
All that stuff in between is simply DIV tags and tables and cells used in the HTML to format the rendering of the web page. It's really rather cumbersome to enter that whole thing every time you want to reference that TextBox and, for that matter, it's not readable. If I'm scanning a test to find stuff, that's a VERY long string.
When you first record the test, you MAY get an Alias that then reads almost exactly like that.
Aliases.Browser.MyPage.Form1.Panel1.Table0.Cell13.Panel2.Table1.Cell23.TextBox
So, the totally COOL feature of Aliases is that, because the Aliase REFERENCE the Mapped object, in Aliases, I can drag TextBox to be a direct child of MyPage and then delete the Aliases for everything else, PRESERVING the Mapped Object. So, the Mapped Object remains as is... and now the Alias reads as
Aliases.Browser.MyPage.TextBox
The object hasn't changed... the Mapped Object hasn't changed. Only the organization of the Alias has changed for the purpose of readability and convenience.
This works for Desktop, Web, and Mobile applications in TestComplete. Again, the article explains it all. The logic is like so:
1) The test makes a reference Aliases.Browser.MyPage.TextBox
2) The NameMapping Engine of TestComplete looks at the Alias and finds that it references NameMapping.Sys.Browser.MyPage.Form1.Panel1.Table0.Cell13.Panel2.Table1.Cell23.TextBox
3) The NameMapping Engine then uses the NameMapping Mapped Object to perform its task of finding and identifying the object
4) The object handle is passed back to the test, via the Alias, so the test can interact with it.