The Query tab is used for agents (and smart adornments) only.
The main input box is used for adding or editing a query ($AgentQuery). Pressing the Return key commits any changes made and runs (or updates) the query. The code box has auto-completion for action code and attribute names (based on using a $-prefix).
The number of items currently matching the query, i.e. the child count of the agent is show at top right.
[Feature removed from v7.5.0, as .contains and .icontains give better control. Case insensitive. If ticked (the default) any comparisons of string values are case sensitive [sic]. This setting is effectively a legacy compatibility control. This is best left as default and sensitivity controlled by choosing use of .contains() versus .icontains() as appropriate. Sets $AgentCaseSensitive.]
Note that an agent's query, action and priority can also be set from the agent tab of the Get Info pop-over.