The feature requires that both devices be running Windows 10 and have this build installed. It works over Bluetooth; if Near Share is enabled for your PC, you'll see a share icon in the apps you use (or you can right-click and choose the Share option in Windows Explorer.) After you click on it, you'll see a list of devices in Bluetooth range that you can share to. After the recipient accepts the file, it'll appear on their computer. It's worth noting that Google is working on a similar feature.
The new build for Windows also includes other features, such as the option to mute a tab that is playing audio in Microsoft Edge, the option to limit the bandwith that Windows Update uses, improvements to Books context menus, and more. You can see the full list of updates at Microsoft's blog.