What is Index in sql server? It's purpose?

Indexes in databases are similar to indexes in books. In a database, an index allows the database program to find data in a table without scanning the entire table. An index in a database is a list of values in a table with the storage locations of rows in the table that contain each value.
 
Indexes can be created on either a single column or a combination of columns in a table and are implemented in the form of B-trees. 

An index contains an entry with one or more columns (the search key) from each row in a table. A B-tree is sorted on the search key, and can be searched efficiently on any leading subset of the search key. 

For example, an index on columns A, B, C can be searched efficiently on A, on A, B, and A, B, C.