感觉好多了 can be translated to English as "feel much better" or "feel much improved." This phrase is often used to describe a situation in which a person is feeling healthier or more comfortable than they were before.

For example, you might say "我感觉好多了，谢谢你的关心" (I feel much better, thank you for your concern) or "昨晚没睡好，但今天感觉好多了" (I didn't sleep well last night, but I feel much better today).

It is not clear where this phrase originated, but it is commonly used in spoken Chinese to describe a feeling of improvement or relief.