I’ve been asked about the legal significance of the various “declarations” filed in the case. As long as I’m answering, I thought I might as well answer publicly.
In short, a declaration, as a document filed with a court, is just evidence. It’s presented so that the evidence is available to the court. The key word is “available.” It’s subject to the other rules governing the receipt of evidence: e.g., there must be a reason to believe the author actually has knowledge of what she says, the fact-finder might decide not to believe what she says, and so on. But assuming it gets past those other hurdles, the court can use the facts the author asserts in support of its decision. Like testimony in court or physical exhibits, a declaration provides evidentiary support.
You also can’t generally just make up stuff and put it in a declaration. The author typically signs it on oath under penalty of perjury, and the lawyer submitting it takes responsibility for not knowingly presenting falsehoods to the court.