Argumentum ad ignorantium means "argument from ignorance". This fallacy occurs whenever it is argued that something must be true simply because it has not been proved false. Or, equivalently, when it is argued that something must be false because it has not been proved true. (Note that this is not the same as assuming that something is false until it has been proved true, a basic scientific principle.)
Examples:
"Of course the Bible is true. Nobody can prove otherwise."
"Of course telepathy and other psychic phenomena do not exist. Nobody has shown any proof that they are real."
Note that this fallacy does not apply in a court of law, where one is generally assumed innocent until proven guilty.
Also, in scientific investigation if it is known that an event would produce certain evidence of its having occurred, the absence of such evidence can validly be used to infer that the event did not occur.
For example:
"A flood as described in the Bible would require an enormous volume of water to be present on the earth. The earth does not have a tenth as much water, even if we count that which is frozen into ice at the poles. Therefore no such flood occurred."
In science, we can validly assume from lack of evidence that something has not occurred. We cannot conclude with certainty that it has not occurred, however.