What does "dirty computer" mean in Slack's About box
Solution 1:
Dirty Computer is probably a Code name for the software release of the Slack client. Developers like to name projects or code they are working on without having to worry about the marketing version or release dates. People also find it easier to remember unique names over numbers. This also facilitates better inter-team communication, as in 'Testers found a defect in Edgy Eft, but developers have fixed it in Feisty Fawn').
For the Slack client, Dirty Computer may use the 'D' in Dirty to indicate the 4th release ('D' being the 4th letter of the English alphabet). The prior release of the Slack client was Cartoon Hero ('C' being the 3rd letter of the English alphabet). Cartoon Hero is a music album by the EDM artist Laszlo. Dirty Computer is a music album by the artist Janelle Monáe.
Other software companies use code names:
Android releases use dessert names in alphabetical (mostly) order - https://en.wikipedia.org/wiki/Android_version_history
Apple releases have internal and external names - https://en.wikipedia.org/wiki/MacOS_version_history
The Linux kernal uses animals - https://en.wikipedia.org/wiki/List_of_Linux_kernel_names
Ubuntu ejoys making animal alliterations and even has a page describing the animal class/family - https://wiki.ubuntu.com/DevelopmentCodeNames
The wikipedia has an article some background on code names in other uses, https://en.wikipedia.org/wiki/Code_name
Solution 2:
I assume that this is an inside joke from the Slack team by an admirer of Janelle Monáe.
See Wikipedia Dirty Computer.