It's safe to assume most of the people reading this work in or administer a Windows-centric desktop environment.
I say "most" and not "all" because some enterprise desktops use other operating systems for various applications. I speak most specifically of Linux, which began as a server operating system but has made inroads with Linux desktop environments. Here are some of the things that Linux and some of its brethren, such as FreeBSD, offer enterprise desktops.
Linux desktop licensing costs and support
This is the most commonly cited advantage to using Linux, either as a desktop or as a server OS. Most distributions of Linux have no licensing fees; you can set up and use as many instances of the product as needed and pay nothing up front. It's a handy way to make a given system functional without spending money on a software license.
A Linux desktop distribution typically includes productivity software (OpenOffice or LibreOffice), a Web browser (Firefox or sometimes Google Chromium) and a number of other apps that should be familiar to most users.
However, using Linux in this fashion means you're entirely on your own with it. If something goes wrong, the creator of the distribution is under no obligation to help you. You can find help online via a support forum -- either one the distributor runs, or on a general support site like ServerFault -- but again, in the end you're on your own.
If you really need proper support for a Linux desktop environment, you can purchase it from the creator of the distribution or from a consultant or other qualified party.
The best Linux apps for compatibility
As hinted at above, the vast majority of the applications that run well on Linux are open source apps. It's best to obtain them through the application repository for whichever distribution is being used. Open source apps are widely used in enterprises, so depending on your existing software mix, you may find Linux apps that are a close match for what you already have.
Note, however, that very few closed-source, or commercial, applications are built for Linux. The majority of those are enterprise products meant for servers rather than Linux desktop systems (such as those from Oracle).
Linux's design has made it difficult for software vendors to consistently deploy applications, except by targeting specific distributions and revisions of the OS. A few mechanisms exist to run closed-source Windows apps on Linux -- such as Wine -- but no guarantees exist for app compatibility or performance.
Linux and hardware support
Linux and the variants of the Berkeley Standard Distribution of Unix (BSD) maintain drivers for a wide variety of hardware, including devices that no longer have manufacturer support.
Here's an example I encountered: A scanner for which no driver updates had been published for several years was recognized directly by Linux and made useful again. This sort of support is itself a crapshoot, since there's no guarantee that a given device will have support, that its support will be feature-complete or that it will be maintained in a timely fashion.
In the same way, a low-end desktop machine can be repurposed via Linux as a kiosk or as a remote terminal for a more robust cloud-hosted desktop.
Linux and BSD distributions are able to hook into enterprise infrastructures -- for instance, by authenticating against Active Directory -- so they can work where needed.
Note that any back-end compatibility that requires the presence of a specific client application may pose a problem. The biggest example of this is Microsoft Outlook and Microsoft Exchange. Outlook can only be run on Windows (or via Wine; see above) and requires its own licensing, so it might be easiest to use OWA for such a client.
Linux desktops and virtualization
Many Linux distributions can run in virtual containers, including Microsoft's Hyper-V, which has specific accommodations for Linux. In addition, some can serve as virtual containers on the desktop. This could allow a desktop user to run Linux as a host and Windows as a guest, with the reverse also being true. Along with multiboot scenarios, such capabilities mean that a given desktop system doesn't have to be devoted exclusively to Linux if the need arises. It can serve multiple duties as needed.
Desktop Linux is often pitched or conceived of as a substitute for Windows, but it might be best thought of as a companion or flanking offering. Its low initial cost makes it useful in situations where a given piece of hardware needs to be online and at least provisionally functional.
Linux also supports a range of applications that might already be in use in your organization. It's always worth experimenting with in a desktop setting, but only to the degree that it actually provides a cost-effective solution to a problem.