The X axis is Q (not time as I first thought) and the y-axis is P/Q, or in other words, the percentage that the Production rate is of the Cumulative Production.

Take an example:
By the end of the first year of production from your oil well, you are producing at a rate of 1 million barrels a year and have cumulatively produced half a million barrels (you started  with no production at the beginning of the year). Thus, Q=0.5 and P=1, so P/Q=2 (or 200%), and a point at (0.5, 2) is plotted to mark the end of the first year.

By the end of the second year, you are producing at a rate of 1.5 million barrels a year and have produced a cumulative total of (say) 1.7 million barrels.  Thus, the P/Q value would be about 0.88 or 88%, and another point at (1.7, 0.88) is plotted.

This carries on and each point defined as (Q, P/Q) is plotted for each year.

It has been found that if production follows the usual Hubbert curve, then the Hubbert Linearisation graph tends to become linear after a certain period of production, and the linear extrapolation projects down to the x-axis to give the URR.

Of course, if the production curve does not fit a Hubbert curve exactly, then the linearisation also doesn't work very well either (as can be seen from Stuart's graphs above)

I've played around with fictional production curves and their linearisations and I've found that you can make graphs that look like the field has a higher URR. For example if the production keeps ramping up and up and then suddenly collapses, then the linearisation essentially 'drops off'.

I believe a lot of the current production is like that, and even areas like the North Sea will decline faster than the linearisation currently predicts.