Inside a CRT an electron beam moves back and forth across the back of the screen causing dots on the front of the screen to glow which produces an image on the screen?

Inside a CRT an electron beam moves back and forth across the back of the screen causing dots on the front of the screen to glow which produces an image on the screen?
This is essentially correct. The electron beam, which originates at the "back" of the tube at the cathode, is accelerated across the vacuum toward the anode, which is the back of the "screen" in front. The beam passes through the magnetic field set up by the yoke, and this directs the beam "across" the phosphor coating on the front of the tube. The beam is "cut off" and returned to the "starting side" of the screen (retrace), and it is turned back on to trace another line across that phosphor coating. The impact of the accelerated electrons on the phosphor coating causes them to emit light.In a black and white monitor, a black and white image is produced (naturally). In a color monitor, three separate electron gun assemblies are at work, and the beam from each is steared across the screen like in the black and white CRT. But there is a "screen" called a shadow mask inside the tube near the front that is like a "grid" with holes in it. The physical location of the electron guns at the back of the tube (the "neck") will allow the beam, even when it is steared, to only strike a particular color phosphor and not the other phosphors. There are three separate colors being painted with different intensities at each pixel (three tiny "dots" of phosphor, one for each color). The sum of the three color beams is three color pictures so tightly "joined" that the picture looks like a single color picture.