CRT monitors have their image drawn by a scanning electron beam, which lights one little dot on the screen at a time. It starts at the top of the screen and scans one line from left to right, then the next line from left to right, and so on - and it paints the whole screen at least 60 times a second, on modern PCs. But you don't see your monitor image as a tiny racing twinkly dot. This is partly because of the persistence of your vision - the same thing that makes a 24 frame per second movie look smooth. TV screens have higher persistence phosphor than monitors, as you can easily see if you press a torch to the front of a turned-off TV in a darkened room, give it a burst of light, then observe the faintly glowing circle it leaves.
Monitors do the same thing, but fade faster.
You need a 75Hz or better refresh rate to eliminate the flicker. This, combined with the higher persistence phosphor, gives a decently flicker-free display. And, of course, you usually watch TV from far enough away that the screen takes up less of your field of view than does your closely-viewed computer monitor. Smaller images seem to flicker less. 24 frame per second movies, on the other hand, get away with their low frame rate without looking painfully flickery because the whole frame's illuminated in one go each time.