What is the adverbial participle?

Read the following sentence:

Она улыбалась, читая(adverbial participle) книгу. She smiled while reading a book.

Adverbial participle – is a special form of a verb in Russian language. It describes additional action in regard to the main action.
In our sentence «она улыбалась» - is the main action. It is expressed with the verb in the past tense: «улыбалась».
And additional action «читая книгу», says that in this moment she was reading a book. For this purpose we use adverbial participle («читая»).
Additional and main actions always refer to the same actor.

*Sometimes it is said that adverbial participle has features of an adverb. It means it answers on question «как?», «где?», «куда?», «когда?»(how, where, where to, when):
Она улыбалась. Когда? Читая книгу.
She smiled. When? While reading a book.