This $1.90/day is an updated (for inflation basically, more precisely for ICP) of the 1990 World Bank standard of $1/day (actually $31/month).
So it's worth recalling the principles/derivation for the original figure of Ravaillon et al. (1991):
Different societies have different perceptions of what constitutes "poverty,"
reflecting (in part) different overall levels of living. Our aim here is only to
quantify the extent of absolute poverty in the developing world, interpreted as
the inability to attain consumption levels which would be deemed adequate in
only the poorest countries. This will leave out many persons who are clearly
deprived relative to others around them. [...]
In principle, one can think of the real poverty line as comprising an
"absolute" component which is constant across all countries, and a "relative"
component, which is specific to each country. In seeking to measure the extent
of absolute poverty one might simply ask: What is the lowest real poverty line
observed in any country? This would seem to be a good indicator of the minimum
acceptable poverty line in assessing absolute poverty. However, the answer may
be quite sensitive to the particular countries surveyed and the inevitable measurement
errors in assessing local poverty lines, and in comparing them across
countries. It will also be influenced by inter-country differences in non-income
factors; a country with good public services benefiting the poor, or a relatively
low-cost climate, will naturally have a lower income poverty line. In the light of
these considerations, a better approach is to try to assess a "typical" poverty line
amongst the poorest countries. To implement this approach empirically in the
next section, we assume that the relative component for any country is largely
determined by its mean private consumption, though we allow the possibility of
other factors (such as access to public services) which may also influence the
poverty line. We will then be able to estimate the poverty line to be found in the poorest country, controlling for these other factors. [...]

The lowest mean consumption amongst the 86 countries studied in the World
Development Report is Somalia at $22 per person per month in 1985 PPP prices.
At this point, [their regression] equation predicts a poverty line of $23, only slightly different
from that of India. Thus, India's poverty line is very close to the poverty line we
would predict for the poorest country, and as such, can be considered a reasonable
lower bound to the range of admissible poverty lines for the developing world.
[...] The $23 line is certainly on the low side of
the range found amongst the poorest dozen or so countries in Figure 2. A more
generous, and more representative, absolute poverty line for low-income countries
is $31, which (to the nearest dollar) is shared by six of the countries in our
sample, namely Indonesia, Bangladesh, Nepal, Kenya, Tanzania, and Morocco and two other countries are close to this figure (Philippines and Pakistan).
The sample of countries used was broadened substantially with the 2005 update:
The new data set on national poverty lines differs from the old (Ravallion,
Datt, and van de Walle 1991) data set in four main respects. First, while the
old data were drawn from sources for the 1980s (with a mean year of 1984),
the new data are all post-1990 (mean of 1999), such that in no case do the
proximate sources overlap. Second, the new data set covers 88 developing
economies (74 with complete data for the subsequent analysis), while the old
data set included only 22 developing economies (plus 11 developed countries).
Third, the old data set used rural poverty lines when there was a choice,
whereas the new one estimates national average lines. Fourth, the old data set
was unrepresentative of Sub-Saharan Africa, with only five countries from that
region (Burundi, Kenya, South Africa, Tanzania, and Zambia), whereas the
new data set has a good spread across regions, including 25 countries in
Sub-Saharan Africa. The proportion of African countries in the old sample was
about half what it should have been to be considered representative of poor
countries. The sample bias in the Ravallion, Datt, and van de Walle data set
was unavoidable at the time (1990), but it can now be corrected.
In this latter model, they ended up using the mean poverty line for the 15 poorest countries as the estimator; the list of these 15 countries was
Malawi, Mali, Ethiopia, Sierra Leone, Niger, Uganda, Gambia,
Rwanda, Guinea-Bissau, Tanzania, Tajikistan, Mozambique, Chad, Nepal and
Ghana
This broadened base (which yielded $1.25/day for 2005) was not without controversy as it implied less than a $1/day in 1993 terms ($0.92 instead of $1.08 which a simple inflation update of the 1990 figure would have given); the number of (extremely) poor people was thus retrospectively increased by some 500 million for 1993.
In contrast the 2011 update was much less revolutionary....
Taking the average of the
same 15 national poverty lines that yielded the $1.25 line in 2005 PPPs, now gives $1.88 per day in 2011 PPPs, which is rounded to $1.90 for ease of communication.