The OR shows how much weight a horse has to carry compared to other horses in the race ...
e.g.
Horse 1 - rated 90
Horse 2 - rated 88
Horse 3 - rated 86
Horse 4 - rated 84
The conditions of the race then set how much physical weight the top rated horse will carry in each race.
This can change from race to race and is not always the same. Lets say in the race above the top weight is set to carry 9st 10lbs
Horse 1 - rated 90 - 9st 10lbs
Horse 2 - rated 88 - 9st 8lbs (rated 2lbs lower)
Horse 3 - rated 86 - 9st 6lbs (rated 2lbs lower)
Horse 4 - rated 84 - 9st 4lbs (rated 2lbs lower)
In the above race .. lets say that horse 4 wins and horse 1 comes second .. the handicapper re-asses the horses and gives Horse 4 an extra 5lb to carry, this horse is now rated 84 +5 = 89, he also gives horse 1 an extra 2lb for finishing so close to the winner.
If all the horses meet again in the next race, the New OR's (official ratings) will look like this
Horse 1 - rated 92
Horse 4 - rated 89
Horse 2 - rated 88
Horse 3 - rated 86
In this race, the conditions say that top weight will carry 10 Stone
So now we have :
Horse 1 - rated 92 - 10 Stone
Horse 4 - rated 89 - 9st 11lbs
Horse 2 - rated 88 - 9st 10lbs
Horse 3 - rated 86 - 9st 8lbs
So horse 4 has gone up 5lb in official rating, but conditions of the race mean he carries 7lb physical weight more.
Other things then add or reduce weight too. Jockeys with claims can reduce weight carried, some races will add weight if a horse has previous wins, sometimes there is a minimum weight set in a race, so a horse might be running "out of the handicap" i.e. having to carry above the weight he should carry because of this minimum. There is also WFA or weight for age .. that is an allowance given to younger horses competing against older in certain races at certain distances .. it changes based on distance of the race and also time of the year.