I don't think it's a meaningless number. Maybe I want to know compare the frequency of two terms, then Google's estimate of results is pretty useful. On the other hand result number 230,000,000 is certainly not useful. Well, it might be a little useful, but there are 229,999,999 documents that Google thinks are more useful to me, so it is a reasonable optimization by Google to not actually prepare a results page for it.
When I'm trying to choose between two alternative spelling or phrasings of a concept, I'll frequently google the two alternatives I'm considering to get a sense for which is more common.
Maybe the user wants to find out if there is more weather data for Sydney, Melbourne or Canberra by comparing the number of results. Sydney has the lead, btw.
Maybe they do, and number of results will give that information. But how does one verify authenticity of that number. For example saying that there were 102,345,290 results returned for a query is of no use if you cannot browse to x result. Google could have just picked these numbers out of proverbial hat. Maybe they already do :)
