What is the water cure? Why does Tom tell Aunt Polly he likes Painkiller? How does it taste? What lesson does Tom teach his Aunt?

 Aunt Polly, concerned with Tom's health, practices a multitude of home-remedies and cure-alls on Tom. Gullible when it comes to quack periodicals and medicine, Polly tries everything from water-treatments to feeding him "Pain-killer." The "Pain-killer" became a regular treatment, and to Tom, it tasted like liquid fire. Tired of the daily doses, one day Tom feeds a spoonful to the cat, which upon receiving the medicine begins to do somersaults in the air while "spreading chaos and destruction in his path." When Polly learns that Tom has fed the cat the painkiller, Tom explains for his actions by saying that he "done it out of pity for [the cat] ­ because he hadn't any aunt" to "burn him out" and "roast his bowels." Polly suddenly feels remorse, seeing that her endless doses of medicine were as much torture for Tom as it was for the cat and the two come to an unspoken understanding.

The water cure....

The water treatment was new, now, and Tom's low condition was a windfall to her. She had him out at daylight every morning, stood him up in the wood-shed and drowned him with a deluge of cold water; then she scrubbed him down with a towel like a file, and so brought him to; then she rolled him up in a wet sheet and put him away under blankets till she sweated his soul clean and "the yellow stains of it came through his pores"—as Tom said.