Transfer a folder with subfolders from PC to Smartphone Note 3 via WLAN
There are a number of programs.  You're described the functionality of an FTP or SMB service.

One of the best is Servers Ultimate.

You might also take a look at Airdroid.

Type this in the file explorer window of your OS to see a GUI resolution:

ftp://192.168.1.150:2121


(The IP address should be replace for the one that Servers Ultimate Pro gives you.)

You'll end up with a regular file browser window where you can drag and drop items between your computer and your Android.

This is a view of your drag/drop (copy option) in Linux:


This is a view of your drag/drop (copy option) in Windows:


The Android is on the left of the two pictures.  The PC is on the right of the two images.

When you drag and drop, you can drag and drop (transfer) full subfolders between the Android and the PC, or of course individual files.

Enable write access for the user:

Ensure you have setup a user for your ftp server and enabled write access for this user.  You can check this by clicking (from Servers Ultimate Pro):


Click on Servers then Click the FTP server you setup
Click Edit
Click General
Click Users
Click the specific user
Put Check mark in Allo write access