WiFi File Transfer is one. There are many others, both Bluetooth (a bit slower) and WiFi, in the Play store, some completely free, some limited unless you pay (WiFi File Transfer is limited in file size until you make the in-app purchase).
You can't really sync folders, though, since folders are a sort of artificial construct - all you can copy is files. As far as continuous sync, about the only way I know of is to the cloud - and the default in Android is to keep pictures and GPM music folders (among others) synced. Someone else may know of some apps to keep folders synced between 2 devices.