Arthur has designed several similar languages, and from what I can tell 'q' (his newest) has superseded 'k'. Much like k was used to program applications in kdb, q is used to program applications in kdb+.
You can download a trial version of kdb+ to play with q... I don't believe you can get kdb/k anymore.
Here is their publicly accessible sample code, which is useful for getting a feel for what k and q are like:
Worth checking out if you need to do timeseries analysis of large tick databases or the like... I know of at least one vendor (to remain nameless) that used it as the datastore behind their webapp with mixed results. It's very easy to develop with and great for certain applications -- but it's a little bit lacking in documentation (to be generous) and there's not a large developer community.
Just my 2 cents...