Yes, you got it pretty much figured out.
When you have a clustered index, then any non-clustered index will also include the column(s) from the clustered index as their "lookup" into the actual data.
If you search for a value in a non-clustered index, and you need to access the remaining columns of the underlying data, then SQL Server does a "bookmark lookup" (or "key lookup") from that non-clustered index into the clustered index (which contains the data itself, in the leaf-level nodes). With a clustered index, you don't need the RID's anymore - and thus you don't have to update all your index pages if a RID changes (when data gets moved from one page to another).
Bookmark lookups are rather expensive operations, so you can add additional columns to your non-clustered indices via the INCLUDE
statement. With this, your non-clustered index will contain those additional columns on its leaf-level pages, and if you only need columns that are contained in that set of data, your query can be satisfied from the non-clustered index itself (in that case, it's called a "covering index") and you can save yourself a series of bookmark lookups.