You probably want to display subtitles below the picture on the black surface?

By default you can only position subtitles inside the picture. That is why when you were experimenting you could not place the subtitles below the picture.

But still there is a way to do what you want using Cropadd video filter.

How to show subtitles under the video in VLC

1) Go to Tools > Preferences and below on the left, in the "Show Settings" section, choose "All ":

2) In the left menu choose Video > Filters > Cropadd :

3) In the "Padd " section enter some positive number for the "Pixels to padd to buttom " option. For this example I used 75px, you are free to experiment.

NOTE
As was noticed in the comments, with the current settings (75px) there is a tiny green line below the video. The solution for getting rid of that tiny green line is simple: enter some even number (for example 76) and there will be no green line below the video. Thanks for this tip to some anonymous user and the community moderator Grace Note who passed this tip in the comments below.

4) Then, again in the left menu, go to Video > Filters and in the "Video filter module " section check the "Video scaling filter " option. The result must be that in the text field below the current section there will be written "croppadd ".

NB!
There are two "Video scaling filter " options to choose from: one in the left and one in the right column. On of them is for another filter - "Swscale". Choose the one, that will give you the word "croppadd" written in the text field below (see the picture):

5) Click "Save " button:

6) Now, for the changes to take effect, you must restart VLC (close it and run again)

That's it.
This way you can customize the position of subtitles so they will be shown outside the picture .

Showcase

DISCLAIMER:
The following screenshots are taken using videos from the Stanford University's learning course
"Algorithms: Design and Analysis, Part 1".
_{NOTE: this course has already transformed into "Algorithms Specialization " as of year 2019.}

BEFORE:

AFTER:

Useful tips

• It is very helpful to assign the related Hotkeys to manipulate subtitles position in real time.
  Go to Tools > Preferences > Hotkeys and assign some hotkey combination for the
  "Subtitle position up " and "Subtitle position down". To do this double-click on the related line and choose some key combination. Don't forget to save and restart VLC player for changes to take effect.
  For instance I have chosen Ctrl+Alt+UP and Ctrl+Alt+DOWN respectively. So now I can dynamically adjust the position of subtitles by moving them up or down while watching a video.
• There are more customization options in the "Subtitles/OSD " section in Preferences, like changing Font, Font size etc, so you can fine tune the subtitles settings according to your needs.

UPDATE (May 2015)

As user akcasoy noted in his comment in the latest (as of May 2015) version 2.2.1 of VLC, the name of the required filter was changed from "Video scaling filter" to "Video cropping filter" (which is actually much more intuitive and relevant).

So here a screenshot for the step 4 if you use the currently latest VLC version 2.2.1:

The height of the video is shrunk by the same factor as the width. I do not see any distortion, it is just a scaling which conserves the aspect ratio of the video. But it would be desirable that the video area is not shrunk. This seems to be impossible with vlc. After the "padding", you can adjust the area of the video by shiftig the window borders. That way, you can obtain approximately the desired result.