Verbal communication is communication with words, and non-verbal communication is communication without words. If you are taking a communication course, it is likely that the focus of non-verbal communication is on body language and facial expression, but there are other means of communicating non-verbally. Let's look at some examples for each category.
Verbal communication is generally divided into oral and written communication, oral being spoken aloud and written being, well, in writing. A spoken conversation is a form of verbal communication that is oral, as is a radio broadcast or a speech. Sign language and Morse Code are forms of verbal communication because they are communicating words, even though they do not fit exactly neatly into oral or written categories. The President's State of the Union address is form of oral verbal communication. Any writing that communicates is a form of verbal communication, an email, a memo, a letter, a book, or poem. I should also note that the words "verbal" and "oral" have had a tendency in recent years to be used interchangeably, but they really are different. Verbal just means using words, so you can see that using words can be aloud or in writing. When we are communicating words with our mouths, that is the precise meaning of "oral."
Non-verbal communication is communication without words. There are many ways we communicate non-verbally. Our facial expressions communicate a great deal without our uttering a single word. We frown, we smile, we sneer, or we maintain a flat affect, and all of these are communicating something to the observer. Our body language also is a means of communication that is non-verbal. We bend closer to the person we are communicating with. Or we move away. We nod or shake our heads. We wriggle around, indicating boredom. We fold our arms across our chests, showing some defense against what is being said. If you watch people in conversation without listening to their words at all, you can usually tell a great deal by observing their body language. Another form of non-verbal communication is purely visual. A painting or a photograph is communicating to us without words, the basis of the idea that a picture is worth a thousand words. When we see logos and symbols, which are common, they, too, are communicating non-verbally, without words. We don't need to see the word "Nike" or the letters "BP" to know that they have made a product. All we need to see is their symbols.
Research has shown that non-verbal communication in the form of facial expression and body language is more "true" than our use of verbal communication. We are capable of uttering words that do not reflect what we think or feel, but we are not so good at concealing thoughts and feelings with our faces and bodies. The implication of this is that it is quite important for us to take note of both verbal and non-verbal communications in our interactions with others.
You can see that both verbal and non-verbal communication are quite important, whether we are the receivers or transmitters of communication. Some understanding of the difference between both helps us to navigate through the world of communication around us.