There are many apps available for Android that allow you to transfer files between devices using a Wi-Fi network, but Samsung has felt the need to release one of its own, which is why it has released an app aptly called Wi-Fi Transfer on the Google Play Store. As the name suggests the app will let you transfer files from a smartphone to a computer over a Wi-Fi network, or between two smartphones or tablets.
You don't need an internet connection for this app to work, instead it lets users a Wi-Fi network to transfer files between devices, so it can really be useful if you want to transfer files on the go. One of the devices starts up a Wi-Fi tethering connection, and the other connects through this network to transfer files, so you don't need a common router access point for the app to work. The process is a bit long-winded for phone-to-phone transfer as Samsung's Wi-Fi Direct share feature works better and faster, but it's great for sending files to a computer quickly.
Since this is a Samsung app it's only going to work with the company's Android handsets, but alternatives are plenty if you don't have a Samsung smartphone. Samsung Wi-Fi Transfer is available for free from the Google Play Store.