As Wikipedia states:
In 2008, the World Bank came out with a revised figure of $1.25 at 2005 purchasing-power parity (PPP).
Wikipedia cites Ravallion, Chen, & 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?