1.
to squint; to narrow one's eyes
To physically narrow one's eyes, typically when looking at something bright or trying to see something at a distance.
2.
to look fondly at; to beam with pleasure
To narrow one's eyes with a smile of affection or pleasure, typically when looking at something or someone dear, such as a grandchild or a beloved scene.
Usage
This expression has two distinct usages. Sense 1 (squinting) is a physical action against bright light or to see better. Sense 2 (looking fondly) describes the warm, pleased expression of someone gazing at something dear to them — the eyes naturally narrow in a gentle smile. Context usually makes the meaning clear.
Similar words
目を細める (sense 2) is similar to 目を輝かせる (eyes sparkling with excitement), but 目を細める conveys gentle, warm affection rather than excitement.