When people say that they're breeding certain flowers together, they usually mean that they're trying to optimize hybrid production. You need at least two flowers to make a pair that can breed together, but most people make plots with several flowers in them to increase their chances. Most people try to breed for certain hybrid flowers.
You've already done the basics by putting the same flowers next to each other, so that's good! Now you just need to figure out the proper pairs to use that will give you special hybrids and how to get a lot of them easily.
To start off with some basic tips, first you should choose some hybrid flowers that you want (just a few for now; don't try to get all at once), and then acquire the flowers you need. You also probably want to switch to Beautiful Ordinance. This lets you only water the flowers you want to hybridize without letting the other flowers die. You want a good-sized plot, but I wouldn't use more than maybe ~12 flowers or so. This goes back to watering the flowers. If you water too many, you won't make any hybrids. It's best to just focus on a few flowers at a time. Water the flowers you wish to breed everyday and always check for hybrids. Once you get a few hybrids, you can breed them together so that they can easily produce more hybrids. That's the bare minimum, but you can also use fertilizer to increase hybrid production, if you have it, though, as with the watering, you shouldn't use more than 1 at a time.
Here are a few guides that list what pairs get which hybrids and how to optimize growth of the hybrids. Let me know if you have any other questions or if anything doesn't make sense! (Sorry for the long post):
Pair Guide 1
Pair Guide 2
Tips and Tricks
