the natural appearance of the skin on a person's face, especially its colour or quality

a dark/fair complexion 黝黑／白皙的肤色

a healthy/clear/spotty complexion 健康／白净／斑斑点点的皮肤

the general character of something

These are radical changes which will alter the complexion of the British contemporary dance scene. 这些变化非常大，将会彻底改变英国当代舞蹈界的格局。

What Pablo has just said puts an entirely/completely new complexion on (= changes) things. 巴勃罗刚刚所说的话使事情发生了彻底的变化。