Nondecreasing order simply refers to the idea of sorting things where subsequent items are greater than, or equal to the previous item. This is different to increasing order because in an increasing ordered list, each item is greater than the previous one.

An example would be the following list of nondecreasing numbers:
-1, 7, 8, 8, 8, 10, 11, 121, 123, 123, 200

Alternatively, an increasing list of numbers would be:
-1, 7, 8, 10, 11, 121, 123, 200

Items don't have to be numerical in nature, just anything that can be placed in some sort of order. Example:

Anna, Ben, Ben, Erica, Erica, Freddy, Jane, Jane, Jane

A nonincreasing definition is similar except that its the other way round, i.e. items are arranged from largest to smallest.