Glucose toxicity refers to the oxidizing and hypertonic (dehydrating) properties of hyperglycemia, both of which continually stress and damage tissues in the body. But the term is also specifically used to refer to the phenomenon of temporary insulin resistance brought on by this tissue stress. 
Glucose toxicity does occur in people,  but it is of high importance to pets--particularly cats. The difference between pets and people is that many pets are not diagnosed and treated until the symptoms of diabetes are impossible to avoid noticing. This means pets can easily go long periods with severe hyperglycemia without much symptomatic notice .
Raises blood glucose -- temporary insulin resistanceEdit
When a diabetic animal is hyperglycemic for long enough, the animal's damaged tissues may start having trouble using insulin. This in turn means that even a well-dosed animal may continue to have high blood sugar, leading to even more insulin resistance.
Various methods through this "glass floor" have been tried, to varying degrees of success. One way is to continue gradually raising insulin dosage until the tissues pick up the insulin and start absorbing glucose, then quickly back off to a lower dose. Aggressive attempts to break glucose toxicity are best regarded as dangerous and should be addressed in close partnership with a diabetes-experienced veterinarian.
These methods may provide relief from glucose toxicity suddenly and unexpectedly, risking overdose and hypoglycemia once the "glass floor" is broken. Caregivers should be vigilant about watching for signs that the floor has broken, such as lower than expected blood glucose levels or a rebound event on a previously "safe" insulin dosage, and be prepared to immediately lower the dosage.
See also the article on regulation difficulties.
Raises insulin requirementsEdit
Glucose toxicity can continue to raise insulin requirements for some time, even after the "glass floor" is broken and blood glucose is brought under control. This effect may take a long time (weeks) to wear off, due to the gradual healing of formerly glucose-damaged tissue.
Glucose toxicity also damages other tissues of the body, particularly capillaries and nerve cells, which leads to neuropathy and in dogs, retinopathy. Damage to other tissues leads to other well known complications of diabetes including kidney malfunctions and (in dogs) cataracts.