"Near poverty" identifies, in this case, children under the age of 18 who live in a family where the poverty level is between 150% and 101% of poverty. So technically they are not in poverty at this time, but considered to be on the edge of poverty, or "near" poverty.
"In poverty" is for children where their family level of income is between the actual the poverty level (100% of the poverty income level) and 51% of the poverty income level.
Children in "deep poverty" are those where families are at 50% or less of the poverty levels. For these families, they are a long ways from getting out of poverty, hence the idea that they are seen as being in "deep" poverty.
The graphic below shows depth of poverty among all children age 17 and under in the region. While a total of around 27% are actually below poverty, you can see how a large portion of the 27% are in deep poverty (11%). In addition, another 16.0% are hovering near poverty.