> So you can see the queen

Even in a small colony, being able to find the queen will make carrying out hive manipulations much quicker and generally a lot less stressful. Many manipulations require you to be able to find the queen so marking her makes her easier to spot. Even if you do not need to know where she is, being able to find her and pop her to one side can give you peace of mind whilst you move things around.

> So you can identify how old she is

If you mark queens in a different colour for different years, you will be able to tell in which year she hatched and therefore determine her age. This will help you to make plans for the colony like requeening and make important observations such as how long she may have left before the bees supersede her or if the reason the colony is dwindling is because she is getting old (or not).  

> So you can see if she has swarmed or been superseded

This sounds counterintuitive – how would you be able to find the coloured spot if the queen has swarmed or been replaced? Well, you can’t. But knowing that the queen in the hive IS marked, you will know that any unmarked queen found in the hive is not the queen you had there originally. This is helpful particularly at times when you haven’t managed to get to the bees in a while and they could have swarmed and requeened or even superseded in between inspections.

> So when she swarms into a bush, you know which hive she came from!

Perhaps combined with using numbers and as long as you have kept good records about which queen is in what hive, this prevents you from having to go through all your colonies to determine where the most recent swarm has come from. You should be able to spot a marked queen fairly easily in a swarm as there are fewer bees and no combs to hide round the back of.

> For breeding

For beekeepers rearing queens of specific strains, using colours as well as numbers can help to keep track of breeding lines.