The snapshots are a copy of the database at a particular point in time, generally the tools work on three snapshots, one for DxDesigner and two for Expedition, so that data can be managed between the schematic and PCB layout (FA/BA data). Other utulities also create snapshots, for example in pre 7.x versions of the software Variant Manager created some snapshots, seen as Sx folders in the file system. Since the introduction of the single file database the snapshots are created internally within the database.
Now to the real point of the question, if you use sheet backup (Backup/Rollback) then each time a sheet is backed up it will create a snapshot so you may rollback to the previous state. If you have automatic sheet backup set in your settings then a snapshot is created every time you open a sheet and for every sheet (backup works per sheet so individuals can rollback changes without affecting other users who may be working concurrently), we also store these so they are perisistent. In this case it is quite easy to find the number of snapshots growing and hence the database size too. Currently the only way to remove the snapshots is to use the Clear Backups command for each sheet to shrink down the database size. We realise this is a little bit tedious to do, so will be introducing some improvements in the management of sheet backup in future releases, at the moment I cannot provide more details than this.
Don't forget that once execute 'Clear Backups' you cannot 'undo' the command to restore them, not that you'd need to in this case. You may choose to disable the 'Create automatic backup' option in the Advanced page of the settings dialog which will prevent the number of snapshots growing rapidly.
As an update to this thread we will be introducing an 'Add in' to manage sheet backups within DxDesigner. The DxDesigner 7.9.3 release highlights presentation covers the features in detail. This will be posted on SupportNet in the next day or so.