Literally it means this night has the shiniest moonlight in this year. "多" means "月光很多",however it does not make any sense,we never say 月光很多,we say 月色很好（the moonlight is pretty beautiful in color,usually it refers to a full moon night),but always keep in mind poem language is changeable,especially in traditional poems.They focused more on synesthesia(I'm not sure if I have used this word right),artistic conception and rhyme. As you can see in the ending part of this poem below: 一年明月今宵多，人生由命非由他。有酒不饮奈明何。How wonderful the moonlight is in this night.Life links to nothing but fate.(So don't worry about the nonsense,let it all go)What a waste of the amazing moonlight if without a drink. "多" and "何" are rhymed.If we change "一年明月今宵多" to"一年明月今宵明“or”一年明月今宵好",it would be more regular in language,but less beautiful in sense.In Chinese,we say "文字的妙用" (an amazing usage of symbols) in this case. Hope it helps.I really happy you are reading traditional poems,cause I really has a deep liking for traditional poems.

一年明月今宵多 Literal translation: one year's moon, tonight's most. By meaning: Of all the moonlights of the year, tonight's the brightest. This is a line from a Tang Dynasty poem.