Super Training is essentially EV training without having to look for specific Pokemon. Each training (HP, Attack, Defense, etc.) increases the corresponding EVs for your Pokemon.
The dark green part of the radial chart reflects your Pokemon's base stats. These cannot be changed and are the same for each Pokemon species. For example, the Mewtwo in that image, like most Mewtwos, has a high Special Attack base stat. The light green portion of the radial chart reflects your current stat distribution, accounting for EVs and level bonuses. The further from the center you get, the higher your stat is in that particular field.
The green bar on the right reflects the total amount of EVs that you have earned. Once your Pokemon fills out that bar, they will not be able to earn any more EVs, either through Super Training or battling other Pokemon. The green bar also affects how many points you get when you connect with shots in Super Training. The higher your bar, the more points, making it a necessity to have a higher green bar if you want to complete the higher levels of Super Training.
Super Training will not increase EVs for a single stat above 252.
Punching bags simply add more EVs. If you do really well in the Super Training (clear quickly), you can get better punching bags which give more EVs. For example, the Attack Bag S only gives 1 Attack EV while the Attack Bag L can give you 12 Attack EVs.
While evolving a Sylveon for a trade, I stumbled upon a solution. Once I was ready to level up my Eevee, I noticed that he too was receiving boosted EXP. As it turns out, I had messed around Pokémon-Amie with Greninja and he ended up with 2 hearts of enjoyment. To verify this hypothesis, I played with a spare Gabite, defeating a wild pokémon after each additional heart.
With a single heart, there was no noticeable change to the Gabite: she still earned normal EXP and didn't seem to have the thelepathic abilities Sylveon displayed. Once she earned her second heart, she immediately started earning boosted EXP. She also starting dancing at the beginning of battle as Greninja had.
Earning two hearts of Affection in Pokémon-Amie will boost EXP earned for the beloved pokémon
Best Answer
Sunny Day causes the weather effect of intense sunlight which alters the way some things work for a few turns:
As Flare Blitz is a fire typed move, its power is increased by 50% by the effects of Sunny Day.