Attached data is a custom field assigned to atoms or brackets. It has an identifier string (name) and a value. Furthermore, a query operator can describe different restrictions in queries.
The dialog provides interface to set the properties of such a field.
Further details of attached data can be found in the Query guide.
Attaching data in MarvinSketch is described here.
The Attach Data dialog is customizable; configuration options and a small example can be found here.