Synching is when Dropbox is catching up with what you have put in it. This help page explains the 'synching' and 'synched' icons, so you don't open the Dropbox folder before the files are fully synched.
If you have a lot of photos and don't want them on every device you use Dropbox on, you can turn 'Selective Sync'. This lets you choose what files will synch on what device.