This is the you guys / you polite form. It's the formal verb usage being used here. tu vorbești - you speak (informal) voi vorbiți - you speak (formal)
When in doubt, or not sure which one to use, just stick with the formal form of any verbs.
How come in some sentences pronouns are dropped? Yes, the verb conjugation makes it clear, but in other languages (at least to my knowledge) you say the pronouns for the most part.
It's pretty common in many romance languages, you drop pronouns in Spanish and Italian, too.
Search for „pro-drop language“, it's a class of languages, where pronoun is optional, because the verb form shows clearly who performs the action. Some neighbours of Romanian are also „pro-drop“: Bulgarian and Turkish for example.
Pronouns are generally dropped in Romanian... But not if you want to emphasise the person for any reason.