An evidentiary hearing is one that involves something other than pure attorney argument.
If the hearing is not evidentiary, all that can be done is for the attorneys to argue about facts already in the court record (such as agreed facts or facts already decided by the court) and how the law applies to those facts.
If the hearing is evidentiary, live testimony from witnesses, documents that support your case, and other items may be presented. The court will make determinations as to "what the facts are" at these hearings.
Evidentiary hearings are typically longer, whereas a non-evidentiary hearing might involve just the attorneys meeting with the judge in chambers to argue about what the law says.
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Evidence is presented. That means testimony taken under oath and perhaps documents being taken by the court to consider with the testimony.
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My colleagues are both quite correct -- and you'll want to understand that you will need to be extremely prepared. Evidentiary hearing are a lawyer's sandbox, but getting a lawyer involved will be critical to your success -- partiularly if the other side is represented.
Good luck to you!