$1.25 PPP per day poverty threshold - What precisely does it mean? As Wikipedia states:


  In 2008, the World Bank came out with a revised figure of $1.25 at 2005 purchasing-power parity (PPP).


(Update: In 2015, this was updated to $\$1.90$ at 2015 PPP.)

Wikipedia cites Ravallion, Chen, &amp; Sangraula. "Dollar a Day Revisited", 2009.

Of course, there will always be difficulties with measurement. 

But conceptually, what precisely is this $\$1.25$ figure meant to capture? 

Does it mean the equivalent of someone having to pay for absolutely everything (food, water, shelter, utilities, transport, education, etc.) with just $\$1.25$ a day, in a place where prices are similar to those of the US average in 2005? Or something else?
A partial answer : I m not sure what measurement the World Bank would recommend, but I suspect that in practice, the expenses that are taken into account to measure whether one is below or above the 1.25$ threshold vary from one study to another. 

For instance in their famous The Economic Lives of the Poor, Banerjee and Duflo write


  "From each of these surveys we identified the extremely poor as those living in households where the consumption per capita is less than \$1.08 per person per day, as well as the merely “poor” defined as those who live under \$2.16 a day using the PPP in year 1993 as benchmark.3 The use of consumption, rather than income, is motivated by the better quality of the consumption data in these surveys (Deaton, 2004)."


The use of "consumption per capita" suggest that capital income, such as the benefits one get from owning her own house, would not be taken into account. 
Because data quality considerations seem to enter the picture, it opens the door to much variation from one study to the other. 

The above quote however suggests that at equal data quality, income data would be preferred.