Color management gives a possiblity to have onscreen what colors the camera saw and also transfer the same possiblity forward when you give the image elsewhere. If you edited the colors on your computer before you give the image forward, the next watcher have a possiblity to see the same that was on your screen after the edits.
In addition you have a possiblity to see onscreen what CMYK printing would produce. That's essential in print production because CMYK print process cannot show all colors that you can see onscreen, there's more limited color range (=your screen can show much more brighter and saturated colors than CMYK prints, usual term for unprintable colors is "out of gamut").
With color management you have a possiblity to adjust your photo to fit into the used CMYK printing process and see acceptably a reliable preview (=proof) what will be printed.
I wrote "a possiblity" because you can switch the color management off. In addition you or others can have inferior screens which do not obey sRGB nor have any calibrated color profiles to correct with color management the colors they display. Finally one can use wrong color profiles. For example you will print on newspaper and watch the result onscreen as it would be printed onto best white glossy paper. In this case your client can have something nasty to say when he sees the result.
Many applications even do not have color management. At least CMYK printing will be a gamble without color management. If you work only for RGB screens, you can well succeed without color management if you stick with sRGB color range (its a bit narrower than Adobe RGB). That's because most computer screens today can show the sRGB range acceptably altough surely a little differently, but without smudging the colors too messy.
If the popping warning dialog bothers you, I recommend the following with RGB images:
1) Set working RGB space = sRGB
2) Set Color management policy for RGB = Convert to working RGB
3) Deselect all askings
This way you output images with sRGB range.
NOTE: This approach is useless if you work with CMYK or want to preserve the wider than sRGB color range of best cameras. In these cases your only option is to learn the color management theory and the needed practices.
Adobe's software is high priced because people are willing to pay for it. Many do so because the color management and its consistency between different Adobe's applications has proven its usefulness in everyday work.