Learn Romanian: Ei o respectă pe șefa lor.

o is a short pronoun meaning "her". Because the direct object (șefa lor) is a specific person, Romanian grammar requires this "double marking." You must use both the short pronoun (o) before the verb and the marker pe before the noun. Literally, it is like saying "They her respect pe their boss.".

What does pe mean in this sentence?

In this context, pe does not translate to anything in English. It is simply a grammatical marker placed before a direct object when that object is a specific human being (like a boss, a relative, or someone's name).

Could I just say "Ei respectă șefa lor" without o and pe?

No, that would sound incorrect in Romanian. While you don't use pe for objects or general concepts, specific human targets of an action must have this double structure: the matching short pronoun (o for a female) and the pe marker.

If the word for female boss is șefă, why is it written here as șefa?

șefa means "the boss" (the basic noun șefă plus the definite article -a at the end). In Romanian, when you use a possessive word like lor (their) after a noun, that noun is required to have its "the" ending attached to it.