The shape of a character's eyes usually has something to do with their personality.
This trope is a while in the making. You can see a relevant TRS thread here. If you have any suggestions for another example, run it through me in the comments, I'll let you know whether it fits. Afterwards, please tell me which part is unclear, if you suggested something that didn't make it. Up for Grabs.
One of the most noticeable visual aspects of a character are their eyes, and in fiction, certain personality traits are more commonly attributed to specific eye shapes. When a character is rendered visually with an unusual eye shape, that's usually an indication of a specific personality trait in that character. Eyelashes also contribute to the profile of the eye as it appears to the viewer, permitting for varying amounts of sharpness, definition, size, and expression. This mostly comes in a few different flavors. A sharper angle at the upper, outer edge of the eye may be an indicator of high social status, arrogance, pride, assertiveness, intelligence, a reserved personality, and aggressive tendencies. ActionGirls are more likely to have this eye type, as are tomboyish females, and characters of particularly fiery temper. Darker and Edgier (as well as Evil) characters are also more likely to have this sort of eye. If eyelashes are a major factor of the eye shape, they can also imply a preoccupation with personal beauty, which is closely related to the feminine aspects of Tertiary Sexual Characteristics. Cynical, jaded, and mature characters are all liable to have this appearance as well. A more rounded eye shape implies a soft, submissive, humble, generous, sympathetic, or sincere character. This is common for Non-Action Guys, Damsels In Distress, and other characters who qualify for being The Chick. Rounded eyes have the added effect of appearing younger and in most cases, cuter as well. Characters with this eye shape have the tendency to be less intelligent than characters with sharp eyes. Innocent, immature, or naive characters are particularly likely to have eyes like this. Another aspect of the trope regards the orientation of the eye on the face. In perfectly circular eyes, this doesn't matter, but for eye shapes with greater length than height, there's the factor of whether the outer edge of the eye trends downward or upward. When the outer edge of the eye droops or angles down, it has many of the same implications as a rounded or soft eye, with particularly strong implications of passivity or submissiveness. See also Tareme Eyes. When the outer edge of the eye angles upward, it gives many of the same implications of pointed, or sharp eyes, often with a focus on conceit, a sense of superiority, and the implication of exotic origins. See also Tsurime Eyes. Compare Tsurime Eyes and Tareme Eyes, subtropes applying to a more specific east-asian manifestation of this trend in character design. Examples that fit all the criteria for those tropes should be placed on that page instead.