Mysql indexing explained in few lines

Indexes are used to find rows with specific column values quickly. Without an index, MySQL must begin with the first row and then read through the entire table to find the relevant rows. The larger the table, the more this costs. If the table has an index for the columns in question, MySQL can quickly determine the position to seek to in the middle of the data file without having to look at all the data. If a table has 1,000 rows, this is at least 100 times faster than reading sequentially. If you need to access most of the rows, it is faster to read sequentially, because this minimizes disk seeks

What is indexing?

Indexing is a way of sorting a number of records on multiple fields. 

Creating an index on a field in a table creates another data structure which holds the field value, and pointer to the record it relates to. This index structure is then sorted, allowing Binary Searches to be performed on it.

For further reading:

• http://dev.mysql.com/doc/refman/5.0/en/mysql-indexes.html
• http://stackoverflow.com/questions/1108/how-does-database-indexing-work