Washing
Cleaning, Laundering
noun, verbal noun, の adjective
You wash something to cleanse it by doing the washing and cleaning. You have to do the washing if you really want to get all the dirt out and make your things clean.
洗浄 is a relatively formal, technical word that you'll often see in manuals, product labels, medicine, or industrial contexts. For example, contact lens cleaning solution is called コンタクトレンズの洗浄液, and a dishwasher is called a 食器洗浄機. It's also used metaphorically in terms like 資金洗浄 (money laundering).
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
電気ポットはどうやって洗浄してますか？
How do you clean your hot water dispenser?
エアコンのフィルターは定期的に洗浄しましょう。
Be sure to clean the AC filter regularly.
その口座は資金洗浄に使われていたようです。
That account was seemingly used for money laundering.
食器洗浄機の音がうるさくて眠れません。
The dishwasher is so loud that I can't sleep.