It could mean 'shall we carry on?' or 'shall we continue?' 'shall we go ahead?' or without the question intonation: 'let's carry on / we'll carry on'

Go forward! (literally) Andiamo comes from the verb andare= to go or to move. Avanti is an adverb of movement=ahead, fowards or fowards. If "andiamo avanti" is in the end of the sentence means "continues".