What happens when we create index

You can store your index as a list of fixed-size offsets into the block containing your key data. For example:

+--------------+
| 3            | number of entries
+--------------+
| 16           | offset of first key data
+--------------+
| 24           | offset of second key data
+--------------+
| 39           | offset of third key data
+--------------+
| key one |
+----------------+
| key number two |
+-----------------------+
| this is the third key |
+-----------------------+

(well, the key data would be sorted in a real example, but you get the idea).

Note that this does not necessarily reflect how index blocks are actually constructed in any database. This is merely an example of how you might organise a block of index data where the key data is of variable length.

MySQL can use multiple-column indexes for queries that test all the columns in the index, or queries that test just the first column, the first 2 columns, the first 3 columns, and so on. If you specify the columns in the right order in the index definition, a single composite index can speed up several kinds of queries on the same table.

SELECT * FROM test WHERE first_name='Andrew';

SELECT * FROM test
  WHERE last_name='Smith' OR first_name='Andrew';

Suppose that you issue the following SELECT statement:

mysql> SELECT * FROM tbl_name WHERE col1=val1 AND col2=val2;

If a multiple-column index exists on col1 and col2, the appropriate rows can be fetched directly. If separate single-column indexes exist on col1 and col2, the optimizer attempts to use the Index Merge optimization..

Source: http://dev.mysql.com/doc/refman/5.0/en/multiple-column-indexes.html