Hola amigos,
I had installed an application on my Mac OS X and then found it to be not of any use for me. I moved the application from the ‘Application’ folder to the Trash and then emptied it. It was normal for the Finder to ask for administrator password as I was trying to remove an application file.
Later on, I was deleting some files to free up disk space when I realized that the Finder was again asking for admin password and I could see the Trash empty (I thought it is directly deleting the files without moving it into the Trash; for the time being). I tried on multiple files in different folders and found the same ‘Finder wants to make changes. Enter your password to allow this.’

This popup comes every time you try to move files to Trash or while emptying the Trash.
This problem usually arises because while emptying the Trash, the owner or user privileges gets modified and only the root/administrator can access it.
To fix this problem, simply open up your Terminal and type the following command:
sudo chown your_user_name ~/.Trash
The above command will change owner (chown) of the Trash (location: ~/.Trash; ~ – Home path, .Trash – ‘.’ meaning hidden file) to your ‘user name’ and give read/write permissions to it. We use sudo to give administrator privilege to make the changes and you have to enter your admin password once.
You can also use this command to give access privileges for particular files/folders to other users.
Note: Some users might have also noticed that the Trash is not getting cleared ever after you click ‘Empty the Trash’ and it shows successful. (The above method in not tested yet though for this particular problem, but you can always try it out and share it with everyone here).
Hope this helps you 🙂 Leave your queries in the comment and will get back to you.
Let the Windows be open, and feel the Freedom.