Why does 赤道 mean Equator?
Actually there are three of these words: 赤道, 黄道, 白道, where '赤' means 'red', '黄' means 'yellow', and '白' means 'white'. 

赤道 is the equator. 黄道 is the sun's track in the sky. 白道 is the moon's track in the sky. As for why they are named so - they are named using "the five colors corresponding to five directions", according to 《汉书·天文志》. If you know Chinese, you can refer to this question on 知乎: https://www.zhihu.com/question/21376627