Those filters are expressed using the CQL syntax. It is the same as the formulas in the style definitions.
For example, in the online search and filter demo, there is a layer of African countries. A filter, allowing only opec and unesco countries would look like this:
((OPEC == 1) AND (UNESCO == 1))
In this layer, there are defined attributes with the names "OPEC" and "UNESCO" (case-sensitive!), and both attributes are integers.
An example of a filter on a string attribute would look like this: (NAME LIKE '%dunno%')