These are terms that refer to the number of chromosomes that a plant cells contain. 
Most plants in general are diploid, meaning they have two complete sets of chromosomes. Diploid daylilies (or Dips) have 22 chromosomes, 1 set of eleven from the pod parent and one set of 11 from the pollen parent.
Tetraploid daylilies (Tets) contain 44 chromosomes, essentially giving them twice the amount of genetic material as diploids. This gives the hybridizer more opportunity for 'breaks' or more dramatic advances than can be made with diploids. 
Triploids are not seen often in daylilies. They have a triple set of chromosomes and are generally infertile. 
Louisiana iris diploids have 42 or 44 chromosomes.  That means they get 21 or 22 from each parent.  Humans have 48 chromosomes and get one set of 24 from each parent.
Triploids would have 63 to 66 chromosomes and tetraploids would have 81 or 88 chromosomes and would get 40 to 44 from each parent.