The Himalayas are a range of mountains in Asia, most correctly defined as stretching from the Indus river in Pakistan, through India, Nepal, Bhutan, ending at the Bramaputra River in India. This is often extended to include the Karakoram, the Hindu Kush, and other minor ranges extending from the Pamir Knot, as these mountains are continuous with the Himalaya proper, and the geographical difference makes no difference for the traveller, we follow this convention here. This region includes the 14 highest mountains in the world, and over 100 peaks over 7200m.
If you are not planning to do any trekking, then you will not need any special equipment, or even warm clothing as you will be able to pick up good warm clothing on entry to the region. If you do need warm clothes, don’t miss the second-hand markets selling attire from wealthy nations.
If you are trekking, the equipment you will need depends on your destination, in most of Nepal you will need nothing more than a sleeping bag and a pair of boots; the Indian Himalaya offer a large number of routes that are possible to trek independently if you have a tent, stove, and all the equipment needed for unsupported trekking.