to lay out mean in the following sentence?
She can be seen wiping away tears after breaking down as the case was laid out today.
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Lay out can mean "to describe or explain something clearly" (Longman English Dictionary Online). The dictionary provides the following example:
"The financial considerations are laid out in a booklet called 'How to Borrow Money'.
So what your quotation from the article means is that the woman was overcome by the emotion after hearing the detailed description of the murder she is accused of.
'Case' is being used here in the legal sense, "a set of facts giving rise to a legal claim, or to a defense to a legal claim." (see sense 10b here). 'Laying out' their case is what a lawyer (or legal team) does as they present their arguments and evidence. It's used here in the sense of 'explain or make clear'.