According to Apple, the MagSafe to MagSafe 2 Converter allowed you to “use the MagSafe connector on your LED Cinema Display, Thunderbolt Display, or MagSafe Power Adapter to charge your MagSafe 2-equipped Mac computer.”
Essentially, this adapter helped to bridge the gap to allow original MagSafe power-equipped devices (2006–2012) to be used after Apple changed to a new MagSafe 2 (2012–2019) standard in 2012.
MagSafe was an Apple technology that allowed power cords (primarily on laptops, but also used on some displays) to provide power using a magnetically attached cord. The technology was extremely effective in preventing damage because if a user would, for example, trip over a laptop power cord or forget their device was plugged in, the magnet would pull out of the socket without damaging the device.
Devices that used this adapter included: 24-inch Apple LED Cinema Display, 27-inch Apple LED Cinema Display, Apple Thunderbolt Display, Apple 45W MagSafe Power Adapter, Apple 85W MagSafe Power Adapter, MacBook Pro with Retina display, and MacBook Air with MagSafe 2 power port.