The Indiana Bureau of Motor Vehicles (BMV) states that a SR-50 is a form used by a person to provide proof of current insurance to the Bureau. This form shows the Bureau both the beginning and end dates of the current policy.
So the basic definition of the SR 50 is a form required by Indiana (and possibly a few other states) as proof that one currently has insurance on their vehicle.
For example in IN there is the financial responsibility law which requires all drivers to maintain financial. This law states that a driver must show proof of insurance to the Indiana DMV for any moving violation or accident for which they have been convicted. Once the BMV is notified that they have been convicted of a moving violation or accident, they will send the driver a Certificate of Compliance. The driver's insurance agent or company must fill out this form. This form must be sent back to the BMV within 40 days in order to avoid a mandatory driver's license suspension (Noncompliance Suspension).
If a person is not insured at the time of a violation, they may be subject to a one year suspension of their driving privileges, owe a reinstatement fee of between $150 to $300 and will be required to have an Affidavit of Current Insurance, or SR-50 form, filled out and returned to the BMV by their insurance company.
For clarification a SR 22 is proof of financial responsibility. In Indiana a SR-22 is mandatory three (3) year period if you are required to maintain this certificate of FR.A SR 50 is proof of current financial responsibility that you insurer would send to the state.
The Indiana government site has the Affidavit of Current Insurance "SR-50" form online if you wish to look it over.