An image is a 2d array with each point denoting a color combination of basic RGB (one pixel, basically). So, when it is displayed or relayed to laptop/desktop monitor, how does it work? Is the monitor a 2d array, i.e, if we open up the monitor are we supposed to see any grid structure?
Yes, it is a two dimensional array.
You won't see a grid, as human vision isn't good enough.
Let's engage in gedankenexperiment. Let's pretend your 19" (diagonal) display is 1920x1280, in a 16:9 aspect ratio. (Please substitute your own data for the display diagonal, horizontal, and vertical size.) The line from A to B, or the line c, below is 19".
c^2 = a^2 + b^2 as per the Pythagorean theorem
19*19 = a^2 + b^2
361 = a^2 + b^2 where a = (9/16) times b (derived from our 16:9 aspect ratio)
361 = (9/16)b times (9/16)b + b^2
361= 81/144 times b^2 + b^2
361 = 0.5625 times b^2 + b^2
361 = 1.5625 times b^2
231.04 = b^2
15.2" = b which has 1,920 pixels, so there are 126.3 pixels per inch. You can't see that fine.