Thats an incredibly open ended question for interpretation. Riot recently released a video that highlighted so-called "design points" ... I think there was around 6 in all.
Champions that they pointed out didn't meet these design points were old Urgot and currently Aatrox.
When you play a champion, theres a LONG array of things that pull you into that champion, for me, its like this:
Uniqueness
I want that character to feel unique. The character should have a personality and ability set that define them.
Meta-ness
The character should feel like it could atleast have a place in the meta. I want to be able to make game-changing plays on the characters I'm playing.
Adaptability
The character should be able to build to any situation without having to sacrifice core items. ADC can be somewhat exempt from this, because they're ADCs.
Replayability
This would be a weird one for most people, but it makes sense to me. At no point with a champion do I want to feel like I mastered them. If I mastered them, there feels like there's nothing new to learn and the champion gets kinda stale to play.
I don't know what other peoples core values are like, but this is what I judge champions on on a daily basis when selecting a new character to play.