XXXX requires that submitted work has not been previously published elsewhere, or if it has, that Speakers have obtained permission for its publication by XXXX and will promptly supply wording for crediting the original publication and copyright owner.
Does it mean that I can publish an already published article or not? I don't get it completely.
What it's saying is that if you're submitting something to XXXX for publication that was published previously somewhere else, it requires permission from the original publisher, and the wording for proper attribution, giving credit to the original publisher and copyright owner. So yes, it means you can republish an already published article as long as you have permission and attribute credit.