Many vintage radios and other collectible electronic items use large, expensive 9-volt batteries similar to the one in the second photo. They have contacts which are larger than the ones used today. This adapter lets you use inexpensive contemporary batteries instead. It converts the large contacts to today's smaller ones and provides 9-volts at the proper polarity for your radio or other devices. 

This will let you use a PP3 battery instead of a PP9 Battery

This adapter lets you use contemporary batteries in place of Eveready 266, NEDA 1600, Burgess P6M, Mallory M-1600, Philco P91, RCA VS300A, Ray-O-Vac 1600, Sears 6418 and 6421, Ward 62-96, Wizard 7D7600, and Zenith Z226 and others.

These batteries were used in Bulova 260 Series, Dewald L-414 and M-414, General Electric (GE) P805, P806, P807, P809, P815, P816, and Sonic TR-4, TR-500, TR-66 and others.