Evidential burden is the obligation to produce evidence to properly support an issue. If the evidential burden is not satisfied, that issue cannot stand during a trial.
Evidential burden is different from legal burden.
For example, in a murder trial, if the defendant were to plead self-defence, he would have to satisfy the evidential burden to produce the relevant evidence to support his claim. If he is unable to do so, he would not be able to use this defence. If he is able to do so, the burden would then shift to the prosecution to support their position. In such a case, the legal burden would still be on the prosecution to prove beyond a reasonable doubt that the defendant was not acting in self-defence and committed murder. The legal burden never shifted.
The evidential burden is present so that the prosecution will not have to disprove all imaginable defences. i.e. the defendant cannot claim all defences under the sky and the prosecution will have to disprove them. The defendant can only claim defences that fulfilled the evidential burden. The prosecution will only have to disprove those defences.