Bank statements are printed sheets of paper containing a list of transactions carried out in your bank savings or current account i.e. transactions either deposit of money (credit) or withdrawal of money (debit).
Printed statements of your bank account containing latest transactions (say, for the last 3-6 months) are generally asked for in cases when you are applying for loan viz. loan for car, house, etc. and in cases when you are applying for new/reissue of passport, visa, other official documents, etc. This is for authentication purposes and for evaluating your credit worthiness position, etc.
While many banks have a pre-printed application form, which you'll have to fill in for getting bank statements, some other banks might not have such a facility. In that case, you can submit a written request letter for this purpose.
The following letter template can be used for applying for printed bank statements.