An argument from ignorance is a logical fallacy whereby one attempts to prove a point by claiming there is no proof to a contrary claim. Sasquatch must exist because no one can prove that he doesn't exist. Jimmy Hoffa was abducted by aliens, and we know this because no one can prove that he wasn't.
Often times, an argument from ignorance cuts both ways. The person making the argument can just as easily have his argument turned around against him. Sasquatch doesn't exist because no one can prove that he does. Jimmy Hoffa was not abducted by aliens because no one can prove that he was.
In an argument from ignorance, the premise has no logical relationship to the conclusion. Perhaps Sasquatch does exist, but the inability to disprove his existence doesn't prove he does (premise: we can't prove Sasquatch doesn't exist – conclusion: he must therefore exist). The inability to prove that Jimmy Hoffa was abducted by aliens does not mean that he wasn't.
Other evidence may come along to prove the conclusion true or false. Capturing Sasquatch would prove that he exists. However, not being able to prove that he doesn't exist is not proof that he does. Somehow proving that aliens do not exist would prove that Jimmy Hoffa wasn't abducted by them.
Argument from ignorance should not be confused with similar arguments that are logical. For example, it is impossible to prove a universal negative. Ray Comfort likes to give the example of the claim that there is no gold in China being unprovable. It is easy to prove there is gold in China, all one need to is point to gold in China. However, to know that there is not gold in China, one would have to know the composition of every dental filling, jewelry box, electrical connector, and contents of every bank vault in China. In addition, one would have to know the composition of the soil and rock for every square inch of the third largest nation on Earth (by area). Even if the Communist regime seized every ounce, or flake of gold and moved it all to a secure vault in a Swiss bank account, it could never be proven that they got it all. Lack of proof that it was all gone would not prove that it there was some left though. Finding gold that was missed in seizure would be sufficient proof, however.
Innocent until proven guilty is a legal concept, not a logical one. The inability to prove a suspect guilty of a crime does not prove that he didn't do it, it only renders him legally not legally guilty (OJ Simpson is a classic case in point; millions believe that he killed his ex-wife, despite the prosecution's inability to prove their case beyond a reasonable doubt). Such a legal tradition is merely honored for practical reasons. It recognizes the fact that absolute proof is often unattainable, and offers provisions for inadequate proof.
As long as we're on (or near) the subject of burden of proof, logic requires that the burden of proof be upon the claimant. In the case of legal prosecution, it is the prosecutor that must prove his case. The defense need not prove innocence. It may be prudent to show lack of proof of guilt, but such does not necessarily prove innocence (though it may, as with a solid alibi.) In debates, the burden of proof lies with the person making the claim. If I claim that the Service Employees International Union (SEIU) is a corrupt organization, the burden is upon me to prove their corruption – the burden is not upon them to prove that they are corruption-free.