A Temporary Event Notice (TEN) is a licence that covers you for specific licensable activities, for up to 499 people for up to 168 hours. It is possible to get two TEN licences for two separate events near one another, of 499 people each. For example, one TEN for a marquee and another for a big top. There must be at least 24 hours between temporary events organised by the same person.
For more details on what activities are licensable see licence.
The 168 hours is any 168 consecutive hours; this DOES legally cover e.g. 4pm Friday to 4pm Friday a week later. Some licensing officers may not be aware of the exact text of the law and need reminding.
If your venue has a premises licence that covers the activities in question, you may not need a TEN. This was the case in Nottingham for BJC 2011, which allowed the team to have a BJC longer than (what was then) the legal maximum length of a TEN. But in general it's unusual for a venue in the right price bracket to have a licence covering (e.g.) entertainment outdoors.
Until 2012, the maximum length of a TEN was 96 hours, which is why historically BJCs from 2007 to 2012 have nearly all been exactly 96 hours long.
You do not need a Personal Licence to apply for a TEN.