Search layouts determines which fields are displayed and in what order for various search results.
With search layouts we can customize fields that we want to show in search results, search filter fields, lookup dialogs, the recent records lists on tab home pages in Salesforce Classic.
In Salesforce Classic we can define the search results layout in addition to it we can also define available search results filters.
Click on Setup >> Customize >> Select the object >> Search Layouts
Add the fields from “Available box to Selected box”:
Click on Save button.
Lookup Dialogs layout is used to display the fields when a record is searched from lookup dialog. More information: Lookup Dialogs