This is the first post in what may end up being a series. There's a lot to cover on the topic, but not so much I can't stuff it into a blog. Lets get started.
You probably know what the idea of a linear work flow is already, but for the sake of those that do not, here is a very brief explanation:
A linear work flow exploits the fact that your renderer works internally in float (linear) space. It generates data that 8-bit output clips away, as it is gamma encoded for monitor display. What a shame. That data is very useful in your post-production compositing and color adjusts.
If you are not familiar with the differences between 8-bit, and 32-bit (float) images, or the concept of gamma encoding for display, then you may want to study a bit before progressing. There are some great books out there to get you up to speed. The HDRI Handbook is very well written, and I would recommend it highly. Online, there are a ton of sites that discuss hdri, which in computer graphics, was the beginning of the linear work flow concept. Learn about hdri, and you'll have a much better grasp of the process.
You may wonder what the big deal is, since you've been rendering wonderful images in 8-bit for years. The big deal I suppose, comes down to a few major issues:
1. Physical accuracy
You can be as physically accurate as you want (or have the patience to deal with); all the way to real-world candelas.
2. Realistic lighting
This is a lengthy issue, but lights in CG have traditionally been "cheated" via a linear falloff, or no falloff at all. This is because the linear response of lights are not being properly gamma adjusted in normal work flows. This goes all the way back to how phong and blinn work as estimations of real lighting response. We can and should evolve beyond that with realistic materials that respond to light properly. This is the reason there are so many new MR (architectural) shaders. They are built to respond correctly in a linear work flow.
3. Greater adjustability in post
32float or 16float has the ability to deal with huge color and exposure adjustments. Given a true float compositing environment like Fusion, most filters you use will respond more realistically. Motion blurs, and glows, for example, will behave in a more natural and photographic way.
Others have posted long before this, on the process, but I have found specific information out there lacking, other than in books. So I'd like to discuss it a bit further. One great post that started as a vray-specific tutorial, has slightly expanded to mention maya/MR and others. Thanks to Robert Nederhorst for this link. It also discusses gamma, so if you're not familiar enough with that Greek letter, read this.