Sharing files was introduced in Sync v.2.5. Here you can find the overview of the feature, and this article will cover peculiarities of file sharing on Android.
All shared files and newly created transfers - uploaded and downloaded - appear in the list "Shared links" in Sync menu. Additionally, downloaded files are listed in "Downloads" folder in Sync UI.
To start sharing a file tap on "+" -> Send file. Select the file and then select the app via which this file's link will be sent to other peers. Multi selection is not possible though this flow, and files are to be sent one-by-one.
If you want to share a pack of files at a time, go to your file manager, select the files and from context menu pick 'Send via Sync' (!! Do not use "Add to Sync" menu!!). After that Sync will open with a dialog to select an app for sharing the generated link.
By default the generated link is valid for three days and currently this cannot be changed.
To receive a file tap on "+" -> Scan QR code. BY default files go to Downloads/SyncDownloads directory on internal device's memory. Currently this also cannot be changed. All files located in SyncDownloads folder on the device show up in "Downloads" folder in Sync UI.
Removing file from this "Downloads" folder in Sync UI removes the file from the device as well! Similarly, if you delete the files from SyncDownloads folder, they will be removed from the list from Downloads folder in Sync UI
In "Shared links" menu you can remove it from Sync UI only, and files will remain on the system.