What statement means max friendship

If you are talking about just friendship then yes @Studoku's answer is correct but if you meant the new mechanic in X and Y called Affection, that is a little different.

• Resistant to having stats lowered
• Evasiveness increases
• Similar effect to Endure where stays at 1 hp
• Pokemon levels faster
• More critical hits( says something like ‘Pokemon Meowth is in sync with Trainer Name’)

All of these are permanent when there Affection is full as well, I do believe.

You can only gain affection in Pokémon-Amie by playing with your pokémon and feeding it. When you get enough hearts, the benefits are:

• Increased Exp (1.2x, to be exact)
• Increased chances of dodging a move
• Chance of enduring a move with 1 HP
• Chance of getting rid of a status at the end of a turn
• Increased chance of getting a critical hit

However, happiness (friendship) is earned by leveling it up, giving it certain berries, going to the massage person, and walking around with it. From what I know, the effects are:

• Return does more with more friendship
• Frustration does more with less friendship
• Your pokémon evolves with enough friendship

But however, from my experience, Pokémon-Amie affects happiness as well. My little brother always played with his Kangaskhan and Return was one of its strongest moves. Whenever he got too many Poké Puffs, he would go to his Pidgeot and throw all of the Poké Puffs away because he thought it was funny. When he taught it Return, it didn’t kill a Caterpie. I’m not lying! The Pidgeot’s Frustration was like the Kangaskhan’s Return. What I concluded from this is that Pokémon-Amie slightly affects happiness as wel.