Before I get into the Colour Management options, it is necessary to understand what colour management solves. Colours in a graphic don't look on my monitor the same way they do on yours. On my monitor colours might look more blue, maybe darker, while on your monitor colours might look more red. This is normal. Even amongst monitors of the same brand colours will look different. This is the same also when printing graphics. One printer will differ from the other, even if they are of the same brand. One ink will differ from the other and one type of paper will differ from the other. Colour Management helps you to make sure that colours look the same when viewed on or printed from different devices. Usually you can "record" your colour settings in files called colour profiles which you can give to the person who will receive your graphic, so he/she can view it or print it with the correct colours. For more information, see
Color Management in Photoshop.