A formal tone of voice is more restrained and conventional than informal tones. For example, formal tones of voice in writing tend to avoid contractions and slang. It also typically avoids first- and second-person "I" or "you" statements. You should usually use a formal tone of voice in academic documents, such as essays and exams, as well as professional documents.
In contrast to a formal tone of voice, an informal tone of voice embraces contractions, slang, first-person language and colloquialisms. An informal tone is more similar to how you speak with your friends or send casual emails, although proper grammar, spelling and syntax are still necessary in informal tones of voice. You might use an informal tone of voice in a letter to a friend, memoir writing assignment or magazine article.
A business tone of voice is similar to a formal tone of voice but also implies confidence and sincerity. Business documents usually try to convince the audience of the document's content, so a confident and authoritative --- but not arrogant --- tone of voice is important. Sincerity and politeness are also important to build positive relationships and create rapport. First-person language is often necessary in business communication.
Think about your intended audience, content and goal before you choose a tone. For example, if you're writing an email about a job opening, your tone of voice should be more business-like than an email sent to your best friend. If you're not sure about the tone you should use for an academic assignment, ask your instructor. When in doubt, choose formal language over informal language. After practice, different tones of voice will come naturally as you begin writing.