New files on your Android device will automatically upload to your Dropbox account. And of course, new files uploaded to your Dropbox account will automatically be downloaded to the memory of your device.
In settings, you can choose whether you want the synchronization to upload only, download only, 'upload and then delete' or be a 'mirrored download.' Similarly, you can select the automatic synchronization interval: every 15 minutes, every 30 minutes, every hour, etc.
Dropsync is a very useful app, which allows you to keep your Dropbox account in perfect sync. To upload files greater than 10 MB however, you will need a PREMIUM account, which can be bought directly through the same app.