Index key columns are part of the b-tree of the index. Included columns are not.

Take two indexes:

CREATE INDEX index1 ON table1 (col1, col2, col3)
CREATE INDEX index2 ON table1 (col1) INCLUDE (col2, col3)

index1 is better suited for this kind of query:

SELECT * FROM table1 WHERE col1 = x AND col2 = y AND col3 = z

Whereas index2 is better suited for this kind of query:

SELECT col2, col3 FROM table1 WHERE col1 = x

In the first query, index1 provides a mechanism for quickly identifying the rows of interest. The query will (probably) execute as an index seek, followed by a bookmark lookup to retrieve the full row(s).

In the second query, index2 acts as a covering index. SQL Server doesn‘t have to hit the base table at all, since the index provides all the data it needs to satisfy the query. index1 could also act as a covering index in this case.

If you want a covering index, but don‘t want to add all columns to the b-tree because you don‘t seek on them, or can‘t because they aren‘t an allowed datatype (eg, XML), use the INCLUDE clause.