Any photographer serious enough to consider the full Photoshop program or an alternative should be concerned with color management. Any viable alternative must be able to provide this necessary function.
Every device you use to display your pictures will interpret color differently. This includes monitors, projectors, printers, tablets, etc. The same color codes will look slightly different on the various devices. The description of how a particular device displays color is its color profile. A program with good color management knows how to recognize the profiles of these devices and translate between them so that the photograph looks very similar on each one.
The program must also be able to assign a color space to each photograph. A color space represents the total possible range of colors a photograph might contain. There are 3 predominant color spaces. Each one is suited to a particular purpose in photography. For example, the srgb color space is best for display on the web, with projectors, and printing at many labs online. The Adobe rgb space is better for printing with an inkjet printer. If you have a photo you would like to print yourself and also display online, your program must properly assign the appropriate color space to each version of the photo.
Color Management without Photoshop
As with the other features, is is certainly possible to have good color management without the full Photoshop program. Every full-featured photo editing program has this ability. I will mention a couple of reservations.
Color Management in GIMP
In GIMP, assigning color spaces is a bit clumsy, especially srgb. I am working on a project where I need the srgb space assigned to each image, but despite consulting tutorials my images leave GIMP without a color space, and I have to finish them off in Picture Window Pro. That is OK because I prefer PWP for how it can batch process the last couple of steps.
Color Management in Lightroom
Lightroom works entirely with the ProPhoto rgb color space. This is a very large space that will contain colors that cannot print or be seen on a monitor. You had better know what you are doing when it comes time to export the images to a form that is printed online or viewed on a projector. The family photographer who shoots jpegs and primarily shares on screen or has prints made online is working entirely in srgb. The conversion to ProPhoto rgb and back again is a needless complication for such a person. However, it is not hard to learn what to do, and you need only code it once into your export preset. After that, the press of a button will perform the proper steps for you.