Usefulness of a multi-attribute index

Question

If an index has more than one attribute in it, is there any speed gained in a select statement whose where clause uses one of the attributes in the index?

For example, take a table T with an index on attributes a and b. Is the index useful for the query:

select * from T where a='foo'

I ask because the book I'm reading has the following statement which I have trouble understanding:

If the key for the multiattribute index is really the concatenation of the attributes in some order, then we can even use this index to find all the tuples with a given value in the first of the attributes.