This is one that's been asked for years -- yet, there isn't a simple solution on the internet.
First, get a copy of the PO file for
mate-panel for your locale from the source code.
(On GitHub, click on the file, then the Raw button, then CTRL+S to save to your computer)
For instance, my system's locale is
en_GB. You can check yours with this command:
env | grep "LANG"
poedit -- this is available from the Software Boutique under Programming.
For the rest of this, I'll use
en_GB as an example.
Open Poedit and find the "Applications", "Places", "System" lines and change them to what you want.
Save the new PO file, this will also create a MO file.
Copy the new MO file to the system locales folder:
sudo cp en_GB.mo /usr/share/locale/en_GB/LC_MESSAGES/mate-panel.mo
Then to see these new strings, restart the panel -- Press ALT+F2 and type:
Tip! This technique can be applied to virtually any other program too.