used in spoken English
to want something
-I feel like dinner.
-I felt like I needed that.
feel like doing something: to want to do something
-I feel like asking her.
-I feel like singing.
I felt like asking her.
Like = предлог
like значит 'as if ' = как будто, словно
Like asking her = Предложная фраза, которая функционирует как наречие, отвечая на вопрос, как я почувствовал?
I felt like asking her. = I felt as if I wanted to ask her. I felt as if I might ask her. I wanted to ask her.