I've been playing a lot with Virtual Box recently and have been taking a lot of snapshots. So after taking 3 or 4 snapshots; I felt that the first few snapshots weren't needed anymore. So I decided to delete them. So I go to the Snapshots menu in the right pane[for each machine] and try to delete the snapshot from there. That doesn't work; if there are multiple snapshots and invariably gives you an error saying "There are child snapshots etc attached. Can't delete". That's not the exact message; but effectively you can't delete it.
After Googling a bit, I found that you have to first remove the disk from the Virtual Media Manager. Only once this is done, should you remove the disk from the Snapshots menu on your main screen.
So to do this you go to File - Virtual Media Manager and expand the relevant hard disk. There should be a '+' sign next to it. This'll mean that there are snapshots attached to the disk. Now there could be multiple '+' signs in the form of a tree under your main hard disk. All of those correspond to all your snapshots that you've taken over time.
Now we'll assume that you want to retain only the latest snapshot that you've taken. First restore your Virtual Machine's state to the latest snapshot; you can do this using the Snapshots menu in the main window. Now come back to the Virtual Media Manager.
If you click on each and every item in that entire tree; you'll find that only 1 or 2 items are actually 'attached' to your virtual machine. Those are the only ones that you need. The rest of the items will all be in a 'non-attached' state and can be removed. You can just highlight each of them and then remove them. If you're sure that you don't need them [ like me ;)] you can delete them from the Disk as well, when you're prompted to do so. Deleting them from the disk results in the physical snapshot file getting deleted from the Snapshots directory itself. You can find your configuration in the Settings - General - Advanced menu of your virtual machine (when its turned off)
So once your 'Virtual media manager' is 'clean' you can now go to the Snapshots tab; right click and remove all the snapshots you did not want. VirtualBox will do a few merging operations [I do not know what] and eventually leave you with only the current snapshot.
Hope this helps someone who got stuck like I did. I accidentally cleaned out my entire configuration twice before I got things working :)