Watermelon Island is a small coastal island dominated by a hill, presumably somewhere near Yokohama. The name is earned two-fold: watermelons grow on it year around, and the hill is covered in grasses that give it the appearance of a giant watermelon. Watermelons constantly ripen, fall off into the sea, and are carried to the nearby town with the current, which the town takes advantage of.
Watermelon Island is also a traditional site for practicing swordsmanship. Kendo masters travel to the island to undergo training, which is revealed to consist of standing near a waterfall and pulling on the release for old barricades used to blockade the passage of watermelons in the stream. When the abundance of fruit is then swept out to fall atop the trainee, they aim to slice them all apart in midair with their sword.
Tatewaki Kuno went to this island to train, not for any conscious improvement in his swordsmanship, but to become a greater master of the traditional summertime sport of smashing watermelons the in hopes of impressing girls (primarily Akane Tendo and Ranma Saotome's female form) with his skill. During the training, thanks to a chance accident, Kuno accidentally smashed a melon while it was flying through the air above his head, crushing it onto his skull and giving himself amnesia, though he retained a subconscious instinct to attack watermelons. If confronted by multiple melons at once, he would enter an unthinking berserker-like state, lashing out with such strength and speed that he would create powerful winds capable of destroying all around him, and even when one watermelon was passing by, he felt irresistably compelled to slice it apart. Ranma eventually used this against Kuno and caused him to repeat his initial accident, which restored his memory.
It is unknown if Kuno retains his psychological imprinting to destroy watermelons once his memory is restored, and because of the circumstances, it is unknown if Kuno is able to consciously tap into the great skill he unleashed when experiencing his "watermelon fist". The accident is evidently common enough among trainees on Watermelon Island that the locals aren't surprised when it happens, but it is unknown if other trainees do learn to consciously realise their enhanced speed, power and accuracy without requiring watermelons to trigger it. Presumably they do, given that Watermelon Island is seen as a training ground for swordsmen in general and not "watermelon smashing experts" in particular.