If you know the common carp, Koi fish are their domesticated version. The name itself comes from the Japanese word "carp". The Japanese started breeding Koi fish a long time ago - in the 1820's and they have since bred them into different varieties. You'll get them I different colors - black, red, orange, silver green and even blue.
Outdoors Koi ponds are considered relaxing - the sound of the rippling water especially as it flows through your yard. If the pond owner is quite deliberate about putting attractive plants in, that makes the environment around the pond even more relaxing. The whole point of the plants is to create as natural an environment as possible for the Koi.
There are cases where Koi and plants don't live well together though; this may have to do with the way the pond owner has placed the plants - they should not sit in a pot, but they should be sitting on the pond floor, if possible naturally growing there. When pots are used, the larger fish can knock them over, and once the soil in on the pond floor, the fish start to dig it up. The result of course is murky water and a pond that's that much harder to clean.
If you feel you really want to have potted plants in the pond, there are things you can do to protect them. You can wrap netting over the plant, so that it hugs the pot and the fish can't reach them. Pouring pea gravel on the plants so that when the pot is upset, it doesn't pour the soil all over also helps. If you have large pots, get river stones put inside will make them harder to turn over. And the Koi will also have a harder time reaching the soil - they'll soon give up.
Wondering what flowers would look good in your Koi pond?
Lilies for a start. Just the fact that they come in so many varieties makes them a wonderful option - you can have so many of them sitting in the pond all looking different. And there are varieties that grow in shallow water too, so that should not be a problem - in fact perfect for panting directly at the base of the fish pond.
If you want the ones that grow better in deeper water, you may have to go the pots option to make sure that the fish don't upset them. Deep water lilies have broader leaves which mean more shade for the fish.
Plants have an added advantage too - they attract insects which are good for Koi fish - they are omnivores and insects and larvae are great for them. Koi can be friendly too, and will eat anything, and right out of your hand. If they are fed consistently by one person, they tend to take a liking to that person and will get used to eating out of their hand. Since they are omnivores, share your peas, your lettuce, and even bits of melon that are left over.
Make the outside of your house a great place if you have the ability to. A Koi pond is one way of experiencing nature right at home - they'll make you happy and you'll get the satisfaction of watching them grow.