Why does only half my monitor light up sometimes
There are three possible causes in a situation like this:


An issue with the MacBook Pro
An issue with the monitor
A faulty cable


Trying to identify the problem involves a process of elimination and some patience.

1. MacBook Pro

As a starting point I would reset both the SMC and NVRAM of your MacBook Pro.

RESET SMC


Shut down your computer
Keep the power cable plugged in.
Press at the same time shiftoptioncontrol (on the left side of the keyboard) and the power button
Let go
Turn your computer back on with the power button.


RESET NVRAM


Shut down your computer. 
Press the power button and then press the commandoptionpr keys. You have to make sure you press these keys before the gray screen appears.
Hold those keys down until your Mac reboots again and you here the startup chime.
Let go of the keys and let your Mac reboot normally.


Note: When you log back in you may need to readjust some of your system preferences (e.g. speaker volume, screen resolution, startup disk selection, time zone information, etc).

There may be other things to try (e.g. changing screen resolution, changing mode, etc) but I'd reset the SMC and NVRAM first and try using the monitor as usual to see if that resolves the issue.

2. Monitor

You don't specify your exact model of Samsung monitor, but regardless of model you will be able to reset the monitor. The instructions for doing so will be in your manual. 

Most recent Samsung monitors can be reset by holding down the Source button for about 20 seconds, while older models will have specific instructions. If you don't have your manual, accessing the monitor's Menu and browsing the options should provide a reset option. In some cases you may need to do multiple resets (e.g. Geometry reset, Colour reset, etc).

You can also try changing some of the monitor's other settings to determine what difference this makes.

3. Cable

Testing for a faulty cable is straightforward as it simply involves trying another cable. However, unless you happen to have access to a spare cable, I would try the above steps for your MacBook Pro and monitor first.