An asset is composed of a container, its published attributes and its template. (For more information on templates, see What are container templates?).
While containers themselves do not appear in the scene view, they do appear in many editors. Additionally, if you select an object encapsulated by a container in the scene view, its container can be displayed in the Attribute Editor / Channel Box along with their published attributes. For more information on published attributes, see Published attributes and nodes.
Containers appear in the Hypergraph Connections editor as nodes with beveled edges. If you expand one of these nodes you can see a number of parts: