Color management is a huge subject in its own right, so we won’t go into great detail here. If you’d like to learn more, Jeffrey Friedl wrote an excellent article on color spaces, which you will find at:
In short, we’ve already said that photos are made up of pixels, which each have number values for each of the color channels. For example, 0-0-0 is pure black. 255-255-255 is pure white. The numbers in between are open to interpretation—who decides exactly what color green 10-190-10 equates to? That’s where color profiles come in—they define how those numbers should translate to colors.
Lightroom is internally color-managed, so as long as your monitor is properly calibrated, the only times you need to worry about color spaces are when you’re outputting the photos to other programs. That may be passing the data to Photoshop for further editing, passing the data to a printer driver for printing, or exporting the photos for other purposes, such as email or web.
When considering the size of color spaces, imagine you’re baking a cake, and you need to mix the ingredients. ProPhoto RGB is a big enough mixing bowl that it won’t overflow in the process, whereas sRGB is like the cake tin that just about fits the cake when you’ve finished, but will overflow and lose some of your cake mixture if you try to move it around too much. You use the right bowl for the job.
sRGB is a small color space, but fairly universal. It can’t contain all of the colors that your camera can capture, which will result in some clipping. As it’s a common color space, it’s a good choice for photos that you’re outputting for screen use (web, slideshow, digital photo frame), and many non-pro digital print labs will expect sRGB files too.
Adobe RGB is a slightly bigger color space, which contains more of the colors that your camera can capture, but still clips some colors. Many pro digital print labs will accept Adobe RGB files. It’s also a good choice for setting on your camera if you choose to shoot JPEG rather than the raw file format, if your camera can’t capture in ProPhoto RGB.
ProPhoto RGB is the largest color space that Lightroom offers, and it’s designed for digital photographers. It can contain all of the colors that today’s cameras can capture, with room to spare. The disadvantage is that putting an Adobe RGB or ProPhoto RGB file in a non-color-managed program, such as most web browsers, will give a flat desaturated result. That makes it an excellent choice for editing and archiving, but a poor choice when sending photos to anyone else.
So your chosen color space will depend on the situation. You don’t need to worry while the photo stays in Lightroom, as all of the internal editing is done in a large color space which Lightroom manages. When the photo leaves Lightroom, then you need to make a choice. If you’re sending a photo to Photoshop using the Edit In command, ProPhoto RGB will often be the best choice, retaining as wide a range as possible. ProPhoto RGB doesn’t play well with 8-bit though, because you’d be trying to jam a large gamut into a small bit depth, which can lead to banding, so stick with 16-bit while using ProPhoto RGB. Once you’ve finished your editing, and you want to export the finished photo for a specific purpose, then you can choose a smaller color space.
Whichever color space you choose to use, always embed the profile on Export. A digital photo is just a collection of numbers, and the profile defines how those numbers should be displayed. If there’s no profile, the program has to guess—and often guesses incorrectly. Lightroom always embeds the profile, but Photoshop offers a checkbox in the Save As dialog, which you need to leave checked.