When deleting data you must be very careful and ensure that you are only deleting the data you want to delete. Once it is gone, it is potentially gone for good.
To delete a group AND all of the contacts held within it IE You have a group called Lost leads and you want to delete the 10 people within it. You can simply go to Contacts > Groups and then load up the group which you want to delete (and the contacts held within). Once loaded up so it is displaying the contacts, you will be presented with two red buttons. The first allows you to just delete the group, leaving all of the contacts on your database, the other deletes the group AND the contacts held within it. If you are happy with this, click ok and the system will delete the group AND the contacts held within it