I see René posted while I was typing, but rather than just throw out my "Long...winded" response, here is is anyway...
Can you explain the difference between Adobe RGB (1998) and sRGB IEC61966-2.1 in the Working Spaces - RGB: drop down box?
So, first I'll explain that the different color spaces have different color "gamuts", which governs how the colors are rendered in the program as well as in a conversion to, say, a jpeg/tiff/psd.
What we have are three commonly used color spaces with gamuts that range from "wide", meaning that some colors that tend to be brighter/more saturated are rendered more "accurately" if you have the software and the equipment to "support" that color space (monitor and printer), then to more "narrow"/less "wide" color spaces, that may not quite cover the widest range but have better support from both software and hardware.
We can start with the widest being commonly used, which is a derivative of "ProPhoto RGB". It had been common since the introduction of Lightroom, because Lightroom uses it as its "internal color space". Unlike Photoshop/ACR and DPP, you are "stuck" with this color space (te derivative is called "Melissa RGB). In Lightroom, you only leave this colorspace when doing a conversion/Export (you can specify a color space there) or if you open the image in an external editor, where you also can specify an "output color space.
The key thing here is support for a given color space -- the ability to view it properly in a monitor and with software that can properly "render" the color space/gamut.
Historically, the most common color spaces have been "less wide" than ProPhoto but also better supported. The Adobe RGB color space is the "next" in the scale, and people often use it because for one thing there are an increasing number of monitors that can properly support it and, because modern printers, including many home/office inkjet printers, can handle the brighter/saturated colors that the aRGB gamut can contain. Canon cameras have an sRGB option that they specify can be good for these printers, although they caution people to handle it carefully. But, this applies to shooting jpegs, since Raw images are "handled" by your Raw processor using either the Workplace setting you specify or, with Lightroom, using Melissa.
However, the real-world reality is different from our photo processing->printing workflow. When you are preparing images to put out into the Real World, you are either posting on the Web or in some way sharing photos with family, friends, clients, coworkers, etc. In these situations, you are putting out typically jpegs, and these jpegs will be viewed using a wide variety of viewing software and monitors.
Historically digital photos and hardware/system/software adopted the sRGB color space as a "universal" color space -- it has a "narrower" gamut than aRGB (or of course ProPhoto), meaning that it won't handle the richest, most saturated colors as well but in general, it can be handled "properly" by the various monitors/systems/software out there, meaning they can apply a "standard" rendering with no need to "manage" things by "reading" a color space and applying a special algorithm to "render" the image in that color space.
And, all printers except for some specialize printers can also "brainlessly" handle sRGB images. In fact, some print labs "require" use of the sRGB space.
And so, most of us, those who us especially who post images on the Web, have adopted the practice of sRGB conversion at a well-define point in our workflow. If you print on a device that supports aRGB you may decide to hang onto using aRGB (or, if printing directly from Lightroom or Photoshop you can be in ProPhotoRGB and the software handles whatever conversion is called for) until you need to put images out for the Web or other Real World uses -- so, for example, with Photoshop you can use Save for the Web and it can automatically convert to an sRGB color space, or you can do the conversion manually and do a Save As.
But, many people want to skip the hassle, and so have their Raw converters (DPP and Camera Raw) set to use sRGB and convert automatically to sRGB or, with Lightroom, to Export to sRGB. This is fine, as long as you aren't dealing with those colors that "need" a wider gamut and that you want to be able to print.
If you are not sure, you can switch in DPP and Camera Raw between sRGB and aRGB and, if your monitor is "aRGB-capable" you will see the color rendering. Also, you can see the changes in the RGB histograms, which can give you a clue no matter what your monitor can handle and, in fact, the histograms can be useful to "tone down" colors that are pushing outside the sRGB gamut!