I am currently reading "The Children of The Sky" and I come across this word. "Anguille borkner" seems like some kind of skill. It has been a long time since I read "A Fire Upon the Deep", I don't remember anything related to this word.
Neither anguilles nor borkning are mentioned in A Fire upon the Deep. They're made-up words. Anguille is French for eel and borkner|borkning evokes broken and bork, I have no idea whether any of these resemblances are intended or coincidental. Vinge does not seem to have communicated on the subject. Apparently, it's some skill that we don't have the background to begin comprehending.
If I remember correctly, that section was from a galactic BBS e-mail, and the title said that it was from a race the translators aboard the ship had only anecdotal translations for; also, it is also mentioned that since they're not in 'The Beyond', so the computers aboard the ship aren't working as best they could. For a kick, check out the Tropes website about this: http://tvtropes.org/pmwiki/pmwiki.php/Literature/ZonesOfThought?from=Literature.AFireUponTheDeep I think it mentions the Zones of Thought. I love the series, but how does space affect computer computation? No clue here; must not be sufficiently advanced. ;p lol