Mentioned in despatches means they did something exceptional which was mentioned specifically to regimental headquarters or the ministry of war. This will always be in the service reports of the commanding officer on the day and will therefore go into the individual's service record. You can write to the Regiment of the individual in question and obtain a full copy of their service record which will give most of the details. If the mention in dispatches was obtained in combat, the Internet or historical record will give you some more details. Some regiments are free for service records others will charge about £30.
Not sure if this is the right place for this, but does anyone know if there is a way of finding out why someone would have been recognised for gallant and distinguished services in WWII . I have the notice sent to the London gazette but don't know why and would be interested to find out. Many thanks