They are terms that refer to the number of chromosomes that a daylily cell contains.
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.