Validations used to be a requirement in the rule books for all foreign participants (Non UK DA holders / Non UK Mil PDA holders) to establish that their displays were safe and conformed to the Lateral separation distances as laid down in the then JSP 550 (Now MRP Fly 2000 series RA 2335) / CAP 403 and NATO STANAG 3533. Validations would be carried out in front of the flying control committee and the Display Director, who watch the display make constructive remarks and may suggest the removal or slight alterations, where safe, to adjust the display to conform to the UK regulations in certain circumstances. In many cases including Waddington we still like to validate displays prior to the team or aircraft displaying in front of the public, to ensure that the displays are safe, conform to the regulations and it also provides the crews chance to familiarize themselves with the layout and local area.
The general trend would be and still is that once a display item has displayed in the UK once that year at one venue, the display has then been 'validated'. Although in the current set of regulations there is no formal requirement to do so, it is still seen as a best practice idea as a fall back to ensure all is well with the display, for example the crowd overflight issues last year at Waddington last year with the Thunderbirds.
Farnborough is slightly different and requires all its participants to validate as there are site specific rules and gated heights that must be met over certain parts of the display area, this applies to all participants including the UK based civil and military acts.
A PDA (Public Display Authorisation) for UK military and a civil DA (Display Authorisation) are merely the permission to carry out display flying at given heights, speeds and levels. A military PDA specifies a set routine, which little or no deviation is permitted, without further authorisation and approval from the star level officer, normally the Air Officer commanding the particular group an RAF aircraft belongs to. A civil DA allows a bit more freedom and specifies only an aircraft category (weight/performance), types of manoeuvres permitted, formation, tail chase and leader limits and finally the heights lowest height the pilot is permitted to come down to. It does not prescribe a specific routine.
Hope that helps solve the question. In short it is a final check of a display for safety, not compulsory, but a good idea1