Software
Besides the software, you'd expect to run on any
normal computer (web browser, office applications etc.),
there is plenty more available that makes SBC's an interesting choice:

Linux
Of course, first we have to mention linux.  
Every board manufacturer propably has one or more linux distributions available,
and instructions how to install it, or they refer to raspberrypi.org
The Raspberry Pi is, by far, the most popular SBC.
And so it should, since they got this thing started.

Android
Many of the SBC's can run Android, which opens up a range of Apps, that you can install.
However, it may require some tinkering with settings and such.

Kodi
Kodi will turn a SBC into a media center.
Many of these boards, support 4K video and have a HDMI connection.
Since they are tiny, you could make it dissappear behind your television set.
It opens a new realm of live streams from tv or music stations, through the use of
add-ons, including Netflix and Youtube.
You could also play media from a local file, or computers in the network and, seemingly
record regular television feeds(PVR).
It can be installed on Android and some boards can install Kodi as a dedicated system,
much like a set-top box, with software like: LibreELEC, OSMC, GeeXboX, Xbian or
crosscompile with Buildroot.
But Kodi will not work with all SBC's.

MotionEye OS
This is a complete security suite for a range of (multiple)security camera's.
It includes monitoring, remote viewing, motion detection, streaming, recording,
alert systems and several advanced features.  
You can connect USB web cams or IP camera's.
It is easy to download a zip file from this github address,
It is available for various specific boards , listed on the website.
The advantage of a SBC: It can run for hours on a small power bank, due to
low energy requirements and it's tiny: you can hide it anywhere.
That's what makes it perfectly suitable for security applications.
Thumbs up for this developer ! He's a genius.
Let me remind you: Make a donation for his efforts.
Because, any similar system would cost you a lot more.

WiringPi
This is for the makers amongst us.
If you buy a SBC you will notice the GPIO: General Purpose Input/Output pins.
Wiring Pi is making it easy to use them on a Raspberry Pi.
There propably are other versions for other boards as well.