NowI can't find an exact source of all the walking-pokemon interactions and what they represent in terms of happiness, although from memory once the speech bubbles start to show love hearts, it means it's generally high friendship. I think when your Pokemon dances for joy or hugs you, that represents the highest tier of friendship.
One of the less important game mechanics that is fully understandable without the use of complex equations and such is Happiness. It isn't really the most helpful game mechanic in battle unless you're speaking of the moves Return/Frustration, but it is a game mechanic anyhow. The other use for happiness would be for evolution purposes, which can obviously be an important factor for stats. Anyway, lets start off with some basics.
Logic would suggest that when you catch a Pokmon, it's not going to like you, but it's not going to hate you either. There's a way to increase the Happiness of a Pokmon that you've caught immediately as well, and that's by using a Luxury Ball instead of a regular Pokeball (or any other ball for that matter). Of course, you cant use Luxury Balls on hatched Pokmon, so that shortcut is kinda useless if you are a breeder. There are lots of other ways to influence happiness however, so it's not that important.
So you're probably wondering (or already know) how to check on your Pokmon's happiness without a fancy equation or whatever. Well, you can easily check on it at one of the houses in Verdanturf Town (Ruby/Sapphire/Emerald/OmegaRuby/AlphaSapphire), Daisy in Pallet Town (FireRed/LeafGreen) or a girl in Goldenrod City. There's a lady in one of the houses in that town that will enlighten you on how much your Pokmon likes you. In Unova, there are two people who will give you a Happiness check. In Nacrene City is one who will give you a broad spectrum while in Icirrus City's Pokmon Fan Club is a woman who will give you the details. In Black 2 & White 2, Bianca will give you details too via the Xtransceiver. In X & Y, it's given by a girl in Laverre City and in Sun & Moon you can find the happiness checker in the road of Konikoni City. The statements are as followed
In Diamond, Pearl & Platinum, there is a Poktch application that will show you the happiness of your Pokmon in your party simply by tapping them. It will be shown as hearts. There are various levels including one small heart, two small hearts, two big hearts and two large hearts. The two large hearts being the optimum happiness level. There is also a person, Dr. Footstep in Route 213, who'll give you the footstep ribbon if you show him a Pokmon with maximum happinessSo as for Return/Frustration, they work best when they're happiest/unhappiest respectively. Now seeing as it's so simple to gain happiness, I don't see why you'd want to use Frustration at all. Anyway, they're both Normal attacks and when the happiness is maxed out, the base attack is 104.
From Pokmon Let's Go, Pikachu & Let's Go, Eeve onwards, there are also special bonuses that can happen if friendship is at a certain value. These were tied to affection prior to this but combined with friendshipSpecial Bonuses
To evolve Pokmon via happiness, you must reach 220 it by doing the above efforts, once that is done, you can evolve your Pokmon by making it raise a level either through battle or a Rare Candy. Below are all the Pokmon that evolve through Happiness and what they evolve into:
3a8082e126