What the graph is saying is that for every full degree rise in the 10-year average day time temperature there is a fall in the 10-year average rainfall of 78.8 mm.
At current rates of day time temperature increase in Canberra, which for the last 18 10-year periods have been rising at .087 degrees per year, this means that in 39 years - by the end of 2048 - the 10-year average rainfall in Canberra will be less than 250 mm, which would make Canberra a technical desert.
The period examined is from when records begin, which is 1940, until 2009. The correlation is quite good: an R^2 value of 0.6448.
At present, we are struggling for water, with the current 10-year value more than 100 mm below the average of the whole period. Imagine how bad things will be with rainfall less than half its present value ...
Update: I have just done an error analysis on the slope, including corrects for autocorrelation, and the error is quite large, with two standard deviations giving us a range of -22 mm/degree celsius to -134 mm/degree celsius. Note that there is also error in the slope for temperature. What this means is that a desert could still be a fair way off for Canberra - we might not be a technical desert until around 2170. But it also means that it is equally likely to arrive much more rapidly - we might be a desert by 2035. (note that a reduction in the value of the slope, because it is bounded by zero, increases the range in years much more than an equal increase in value in the slope).