Adverbial participles are built out of a verb (mostly with a suffix), and in most cases they play the role of a sentence element called adverbial in the grammar of some languages (Russian and other Slavic languages, Hungarian, many Eskimo languages, e.g. Sireniki ). It can usually be translated into English by using an appropriate adverbial clause.
Some descriptive grammars treat them as a distinct lexical category, others avoid that and use a more minimalistic approach. Because the above languages have also adjectival participle, the word participle is meant often for both lexical categories.