It's an index that contains two fields. Indexes in general are used for Selection, Joining, Grouping and/or Ordering.
The key thing to realize is that a multi column index is useful from left to right.
For selection, such an index would be quite useful if you had a where clause that looked like
WHERE AWARD_ID = 123 AND CUST_ID = 456
If would also be helpful for
WHERE AWARD_ID = 123
But probably not (directly) helpful for
WHERE CUST_ID = 456
Since the leftmost column of the index (AWARD_ID) is not referenced.
Joining works in a similar manner.
--index useful
FROM TBLA JOIN AWARD USING (AWARD_ID,CUST_ID)
or
FROM TBLA JOIN AWARD USING (AWARD_ID)
--index NOT useful
FROM TBLA JOIN AWARD USING (CUST_ID)
as do ordering and grouping.
If you happen to be using DB2 for IBM i, the following paper is an awesome resource:
http://www-304.ibm.com/partnerworld/wps/servlet/ContentHandler/stg_ast_sys_wp_db2_i_indexing_methods_strategies
If DB2 LUW, the parts about bitmap indexs probably apply, but ignore the information about EVI indexes. Also look at the planning and performance sub-sections Indexes section in the DB2 LUW infocenter
http://pic.dhe.ibm.com/infocenter/db2luw/v10r5/topic/com.ibm.db2.luw.admin.perf.doc/com.ibm.db2.luw.admin.perf.doc-gentopic8.html