Color is one of the most important aspects of photography. It's good to know what your settings should be if you're planning on printing or publishing to the web. This video explains the difference in a simple way.
In my experience, sRGB keeps the colors contained, whether the image is shared online, in an email, or via an app. It's obviously due to the compression and removal of most of the colors, but the advantage is that the image color remains the same. That's the benefit for me.
AdobeRGB has more information contained. If you're planning on printing your photograph, it depends on the printer you'll be printing with, whether you're going to have Photoshop or the printer's software handle the color aspects, which at first was quite intimidating at first. It's also something to pay attention to if you're handing the images off to the creative director who will be laying out the photo in a magazine. It's not that difficult to achieve, but do know that you can basically see the sending of files as part of your workflow, and you'll get better through trial and error, or that's what happened to me.
As professionals, we obviously shoot in raw, so the color space doesn't matter on camera, but, once downloaded and worked through, it's important to keep the color space you've selected throughout the project. You can't go back once you've changed it from AdobeRGB to sRGB. I understand that we usually keep the raw files, but if you've done hours of retouching and coloring, you don't want to have to do it again.