When you have a group selected, the Group button will be checked. By unchecking it you will 'explode' one level of grouping and the objects in your selection can be individually edited. Ungroup is an object-level action i.e. you need to select a group before you can ungroup it.
Unlock is a document-level action. If you check Unlock, all objects in the document can be edited individually whether or not they are a member of a symbol or a group. When a document is unlocked, the construction of groups and symbol is stored so that when you uncheck unlock, the group or symbol will once again behave as a single object.
Unlock is generally used when you want to edit a symbol in your document.