When your site contains fewer than 20 sections, the section selector displayed when you edit an object is a drop-down menu. After this number, SPIP displays an ajax selector which allows you to navigate the tree structure and search for a section by its title.
It is possible to customise the number of sections that trigger the use of the ajax selector by changing the value of the constant _SPIP_SELECT_RUBRIQUES in your config/mes_options.php file (see the article dedicated to it).
Example :
// displaying the ajax selector from 3 sections
define('_SPIP_SELECT_RUBRIQUES', 3);