The search options available on views are defined with a search view. It defines the fields to be searched when typing in the search box It also provides predefined filters that can be activated with a click, and data grouping options for the records on list and kanban views.
Here is a search view for the to-do tasks:
<record id="todo_app.view_filter_todo_task"
model="ir.ui.view">
<field name="name">To-do Task Filter</field>
<field name="model">todo.task</field>
<field name="arch" type="xml">
<search>
<field name="name" filter_domain="['|',
('name','ilike',self),('user_id','ilike',self)]"/>
<field name="user_id"/>
<filter name="filter_not_done" string="Not Done"
domain="[('is_done','=',False)]"/>
<filter name="filter_done" string="Done"
domain="[('is_done','!=',False)]"/>
<separator/>
<filter name="group_user" string...