I'm no biologist so I'll stay away from skull size, capturing more light or others physiological effects that L.Dutch and JBH already covered; instead I will focus on a more psychological aspect.
Big eyes convey a lot of non-verbal communication
Big eyes in animation are a trope because "eyes are the mirror of the soul". This is the part of the body most of us notice first. Also, eyes are capable of conveying a lot of information for someone who can read it: envy, lies, fatigue, sadness... human have evolved to a point where we can understand other's emotions without having even beginning to talk.
My guess is that bigger, anime-style eyes, would be much more mobile and expressive. The average human eye has twelve muscles, and i'm not counting those for the eyelashes, etc. With eyes twice the size, these muscles could provide a lot more of expressions, from the most subtle wink to a full black-eyed pupil.
So, what's the use?
Big eyes convey empathy. When you crave for something, be it a sexual partner or that fancy pair of shoes, your subconcious make your eyes widen, so you can capture more light and see better what caused this sudden urge. And, on the other side, it is known that dilated pupils are considered as more desirable traits when seeking for a mating partner.
But your eyes also widen more when in conflict. This is one of the answers of our body for an imminent fight-or-flee situation: we are aware there is danger and we are already seeking an exit. Showing big eyes with black dilated pupils at this point is telling your opponent: "I am ready to fight" and can be a factor of intimidation. This is why some animals sometimes show "fake eyes", they serve as a way to fool predators into thinking they are staring at the face of an even bigger creature.
Long story short: your big-eyed humans may probably demonstrate more animal behavior, related to instinct, when it comes to seduction or intimidation, and may be able to read other people's emotions much more accurately, to the point it could even look like a form of telepathy.