What is different between children and adults that cause children to forgive so quickly? Today I observed three children at a birthday party become involved in an extremely serious altercation including the use of (toy) weapons.  

Tears were dropping, threats issued, punches and kicks thrown and yet in the space of a few minutes the children had formed a new bond of friendship and were playing contendedly. 

It made me consider the wider social impact; what is it that causes teenage/adult human beings to hold personal grievances and grudges for longer periods of time when children seem so willing to forget past transgressions? 

I am sure there must be a biological mechanism at work from both the child and adult perspective so if any sociologists, child psychologists or behavioural researchers read this forum it would be great to get a detailed answer. 

I suspect similar patterns of behaviour exist in other cub/child/young mammals in social groupings.
The short answer, kids live in the now.  They tend to forget everything quickly.  A child can be crying about their milk being spilled one moment, and playing the next.  They don't think as much about past or future, just what is happening now, and NOW is a big deal.  This can cause problems in some ways, but the plus side is they are quickly side tracked from whatever was bothering them before.

They don't hold grudges for the same reason you can make them forget how fun banging on the trashcan or drawing on the wall was.  The moment something is out of sight it's quickly forgotten.  The offense of 30 seconds ago don't matter, because that was back an eternity ago, and is not NOW.

That 'eternity ago' thing was only half a joke also.  It's been argued that children actually experience time different, because of their length of life and perspective.  A 2 year old has been alive for a tiny fraction as long as it's parent's have, it has less then a tenth the life experience.  However, since they measure time relative to the length of time they have been alive that means that 30 minutes feels like it's 10 times longer to them, because that 30 minutes actually makes up more then 10 times the amount of their life that it does for an adult.  If this is true it explains why a 15 minute wait is an eternity to a young child.  However, it also means that something that happened a day ago feels like it was weeks ago to a young child.  It's easier to forget pass offenses if it feels like they happened in some distant past of time.