In writing or speaking, a sentence using active voice is one that the subject of the sentence acts upon something or someone. For example: "William bought an iPod at the store today." William is the subject, and he is acting on an object (the iPod).
In passive voice, it is the subject that is acted upon rather than the object. The same example in step one can be rephrased in passive voice as the following: "An iPod was bought by William at the store today." William is still the subject of the sentence, but grammatically he is not acting upon the object directly.
Usually, active voice is the preferred method to use. It utilizes less words, is generally more direct and concise, and is a stronger way to state the sentence. Too much passive voice makes papers lengthy and they can see flat or boring. It can also lead to unnecessarily confusing or complex sentences.
There are some times where using passive voice is preferred over active voice. In some types of composition, a rule is to avoid the use of personal pronouns (like "I" or "we"). Particularly, formal writing and scientific papers tend to avoid use of such personal pronouns. For example: "I measured four ounces of water" can be rephased in passive voice as as "Four ounces of water was measured" so not to indicate the "I" pronoun. In these situations, use of passive voice is often necessary.
Another advantageous time to use passive voice is when the subject of the sentence is unknown, or takes away from potential credibility. It is preferable to use passive voice in these situations.
Contrast the following examples:
"Research has been done that proves smoking causes cancer."
"People have done research that proves smoking causes cancer." (Who are these "people" and why should I trust their research?)
The first sentence (passive voice) sounds more credible than the second one (active voice). Without having to mention who "they" or "people" are, passive voice adds reliability to the phrase. The sentence still means the same thing, but passive voice allows complete omission of the subject. This is often used to shift blame off the subject, or to obscure unknown sources of information without sounding unauthoritative.
Of course, it is always better to use proper research and citation procedures for exceptional credibility whenever possible.