The active voice clarifies the acting subject in a given sentence; that is, it makes it very clear who is doing what action in your sentence and at the time you are describing. It helps you avoid using too many prepositional phrases, which can get confusing or tedious for a reader. Additionally, changing from passive to active voice can force you as a writer to be better cognizant of the actors, actions, and objects, in your writing. You'll also be forced to more strongly consider the relationships between different words and phrases in your writing. For example, let's take the sentence, "The eastern armies were forced into submission." Well, who did the forcing? Who were these strong opponents? Don't leave your reader with an unanswered question when you know the answer. Even if you provide the answer, e.g. "The eastern armies were forced into submission by the hordes from the west," it's much simpler and provides more emphasis on this interesting subject to make the sentence active voice: "the hordes from the west forced the eastern armies into submission."
This leads me to answer the other part of your question: when should we use passive voice? If the actor is actually unknown, i.e. you don't have the answer to give your reader, then you should use passive voice. However, writer beware: when writing a research paper or any persuasive essay, you should probably know the answers and therefore provide them. If you don't know who the actor is, you need to explicitly address that fact in your paper. Maybe scholars have not yet determined who really wrote that one work attributed to Shakespeare, or maybe no one knows what split the tree stump in half; in those sorts of cases, you may use the passive voice.
Another very specific use for the passive voice may be that you want to emphasize the ones being acted upon rather than the actor itself. Let's go back to that "Armies" example. If you're writing a paragraph or essay on the eastern armies, you might want to use the passive voice and say "Ultimately, the eastern armies were forced into submission by the western hordes." Technically, the subject of your greater context is the eastern armies, so it makes editorial sense* to leave the sentence in passive voice. This may happen in your or anyone's writing, so bear that in mind when reviewing any written work.
All in all, the active voice makes your writing stronger. Generally, you make a better impression on the reader and give your reader more clarity when you use the active voice, and using the active voice makes you a better writer as it makes you think a bit more (sometimes much more) about what it is that you're writing. A good rule of English writing is this: you know what you're saying, but the reader doesn't. It's your job to make sure they do. The passive voice has its uses, but you should typically only use passive voice when it's absolutely necessary (e.g. subject is truly unknown) or when it makes the most editorial sense to do so.
* Special note: Editing is different from proofreading! Proofreading only involves checking for spelling, grammar and punctuation errors and all their technicalities, but editing refers to evaluating style, word usage (diction), phrasing, vocabulary, tone, mood, wordiness... everything from what you literally said to things in that "it's not what you say, it's how you say it" category. The editorial process can get very lengthy!