Ploidy refers to the number of sets of chromosomes in the nucleus of a cell. In their natural state, most orchids (as well as other plants) have 2 sets of chromosomes (one set from each parent) and are referred to as diploid (2N). Either through chance breeding or conversion in nature, intentional breeding in horticulture or chemical manipulation, other combinations can occur. Of most interest in horticulture are triploid (3N) and tetraploid (4N) states. Polyploid (having more than 2 sets of chromosomes) plants have larger cells and stomata than diploid plants but have a slower growh rate and may have reduced fertility.

Tetraploids are usually more vigorous and show larger growth with thicker leaves as well as larger and heavier substance flowers. They may have a slightly lower fertility, but they do breed. Triploid plants are formed when a cross is made between a 2N and a 4N plant. These plants tend to have the vigor and heavy substance of a polyploid plant, but rarely produce viable seed. A very desirable trait when you want a seedless watermelon, but not so desirable if you want to breed with the plant.

Crosses that have been marked as "treated for ploidy" have been treated chemically at the protocorm stage with a chemical known to change the chromosome count in the hope of getting tetraploid (4N) plants. As growth proceeds there is usually a marked difference between the rate of growth of treated seedlings compared to the untreated seedlings of the same parentage. Not all treated seedlings convert to 4N. I cannot check ploidy at this time, so I make no guarantees.

References: Wikipedia and Breeding of Horticultural Crops: Principles and Practices by N. Kumar