How to quickly analyze board content for specific criteria?

This is best done via the search option and filter box, both located in the top right corner of a board view. The always-open box is for filtering the current board view, and you can search through all boards by opening a search with the magnifying glass icon.

For filters, you can either type text into the filter field to look for specific items on the board, or you can use the built-in filters: Filter for Tasks Updated Today