Peculiar behaviour of code displaying button presses using MSP430
Why is this happening? When I am not pressing the button isn't its state LOW? 


I think there's some incorrect documentation. If you followed the schematic from the link you provided, then when the button is not pressed, the state would HIGH. 



The code explanation says 


  If the buttonState is HIGH, it means that push button was pressed else it is not. Whenever the button state is HIGH, the Green LED is accordingly switched ON else it is switched OFF.


But this isnt the case. The hardware says when the button is pressed, the button state will be LOW. 

What they did was copy the arduino button tutorial and just modified it slightly for use with the Energia board. If you look at the Arduino schematic, it's more inline with what you are expecting. So their code description is incorrect.



If you use the Energia schematic, then you need to be using LOW and if you are using the Arduino schematic then you need to be using HIGH.