We were promised jetpacks, but I'll take Tilemill as a temporary replacement: http://mapbox.com/tilemill/
The MapBox/DevelopmentSeed team has created one of the the last pieces really needed for mainstream open source GIS to gain really massive appeal
TileMill is used for making web maps - or more specifically - for generating tiles that make up the now-ubiquiteous slippy maps we see online.
There are other desktop applications that do this, the most notable being ArcGIS Desktop. But Desktop was built for other things first: advanced analysis tools, some pretty powerful editing capabilities, and authoring paper maps.
TileMill does one thing and it does it well. It costs nothing (compared to several thousand for some flavor of ArcMap), and outputs an open tile format that you can wire up to a webmap or iPad in less time than it takes to install ArcMap.
And it is smooth. The user experience is the best I have had with a desktop application in a long while.
It also has sane, plaintext css-like styling (MSS). This may sound like a no-brainer, but your options before this were basically some proprietary binary format from ESRI (not extensible, difficult to automate, limiting, vendor specific) or SLD, which is open source but widely regarded as something of a mess for other reasons.
There is also the training issue. ArcMap is giant and powerful - and extremely complex. The market for "GIS Analysts" is still strong in a large part because of this complexity. Less experienced users will find TillMill easier to pick up and web designers (of which there is a large pool of talent) will find it very easy.
It is out for every operating system of note.
Seriously, go give it a try.
What else is needed
Conversion - minimal, well documented, mostly automated steps from ESRI - TileMill/FOSS
Samples like crazy - more or less emulate the ESRI samples, complete with documentation