how does multiple column index work in details
This is not necessarily the case. Oracle, for example, has an access path known as an "index skip scan". See http://docs.oracle.com/cd/B10501_01/server.920/a96533/optimops.htm#51553

Basically, if there are few distinct values in column A, and the query restricts on column B (and optionally, column C), the executor will substitute each of the distinct values of column A in turn and probe the index for the supplied value of column B (and optionally, column C).

Postgresql can do something similar, but it is still labelled as an "index scan", see Working of indexes in PostgreSQL