The median is the sample literally "in the middle". 50% of the other samples will be less, and 50% of the samples will be more.
Perhaps they meant "mean", or more specifically: the "arithmetic mean". Most people call this the "average".
An example: given the numbers 1,2,10,11,12,
The median is 11.
The mean is 7.2.
26% are at less than HALF the median income. That was the standard used. Not the median income.
I don’t agree that this is a very useful metric, but thats what they are using.
Putting it into real numbers: the median household income in the US was $51,939 in 2013. So, 50% of that would be $25,970.
The US HHS doesn't have a single number: it varies by family size. In 2015, the closest to the "poverty level" above is $24,250 for a family of 4, in the continental US (AL and HI are higher).
It’s 26% who are earning less than half of the median income.