It is the kidney's job to filter toxins from the blood, and each kidney contains thousands of microsopic filtration units called nephrons. Like all cells, nephrons have a finite lifespan. They cannot regenerate - your pets (and you) are born with an absolute number of nephrons, and once they're gone, they're gone.
Chronic renal failure, or chronic kidney disease, is common in older pets. Kidneys filter out toxins and excrete them with water into the urine. When the kidneys start to slow down, they use more and more water to dilute the blood's toxins. This leads to larger volumes of urine, which leads to increased thirst and water intake. Most pets with chronic kidney disease display increased thirst well before other symptoms emerge.