Widgets are little bits of code that you put into "containers" to add something to your web pages. You can add, remove and reorder widgets from the Blog settings->Widgets tab in the admin interface.
Each container appears in a specific place in a template, typically the header area, sidebar, and footer area are containers. If you change your blog template, the new template may not use the same containers as the previous one. Make sure you place your widgets in containers that exist in the specific template you are using.
Your template may or may not have widgets pre-selected by the template author. If it does not, then $s will provide widgets ... if the template has containers with names it expects. Widgets can also be "hard-coded" into your template, meaning no container is used. Blog A header is an example of this: the title and long description are coded widgets.