What it doesn't mean is that these people are living on what $1.25 could buy in, say, Kenya. If you thought that, then you might think that $1.25 isn't so bad, because money goes much further in developing countries.
Unfortunately, the fact that the money goes further in such countries has already been taken into account. What "$1.25 per day" means is: people living on this amount consume the goods equivalent of what $1.25 could buy in the US in 2005. That is to say, the figure is purchasing power parity (PPP) adjusted. That means we can work out how much, in actual money, people in Kenya live on below this line. In 2005, the purchasing power parity conversion factor was US$1 to 29.5 Kenyan Shillings. So $1.25 is about 37 Kenyan Shillings. At market exchange rate (today's rate, so again this is only a rough estimate), that's 44¢.
Because that's still talking about 2005 money, we want to adjust for inflation, so, assuming 3% inflation per year (again, keeping it rough), that's 56¢. So, in my view more accurately, we should say that the global poor, in Kenya at least - though other countries at an equivalent level of economic development have similar PPP conversion factors - live on 56¢ per day. Jeez.
However, the story doesn't end there, because "$1.25/day" doesn't refer to income. It is based on measurements of consumption. So when a person gather sticks from the forest for their own use - that counts as 'consumption'. Similarly, as far as I understand it, any free services provided by the government count in this as well.
So I think a more intuitive way to think about extreme poverty is: if you gave a Kenyan living below that poverty line 56¢, you'd have doubled what they can consume in a day.
A lot of people who know this about the $1.25 a day line subsequently refuse to believe it. I really struggle to believe it. Surely, if someone lived in the US on $1.25 a day, they would die! (I heard this argued in a conference on poverty by an academic who'd written several articles on poverty.)
If we're referring to income, I think that's simply not true. With an income of $1.25 a day you could have a much better quality of life than the extremely poor. You can dumpster dive and live off the excess of the affluent country; they have free access to roads and lighting, a good legal system and police protection, and medical assistance if they get sick. I know someone who lived on $1000 per year for a couple of years - several times more than the extreme poor, but he had a really pretty reasonable quality of life.
However, if you're thinking about consumption rather than income (as you should), there is a difference which does make the comparison to "$1.25 living in the US" misleading: in the US you just can't buy the sort of low-quality goods that you can in developing countries. Markets just don't exist for those goods. Even the most basic lentils and rice sold at Walmart in the US would be regarded as a luxury item for people living on $1.25 a day.