The left icon displays everything that cannot be displayed by your monitor, any colors that are out of gamut for your display. You do not have to make any corrections to those colors, it is just a warning for you to consider that these colors that you see are not necessarily the same which a different person might see if they had a better screen than you have.
The right icon displays everything that cannot be correctly displayed or printed on a defined output profile or paper. That defined output can have both, either a smaller or a bigger gamut than your monitor. That is for softproofing, you can verify which colors will look exactly like those on your monitor and which ones might look a bit different.
In both cases, it does not necessarily mean that you have to apply any corrections. The output might still look fine. It just is an information to you that in those colors where the warnings are active, you are basically editing a bit blindly.