Ye is short for Ye Su, which is the transliterated name for Jesus.
The character ye (pronounced in the first tone as in the transliteration of Jesus) does not have a special meaning. It is a character used to imitate a sound, often used for transliteration of foreign names. In old Chinese literature, ye (pronounced in the second tone) is the same as father or used to indicate a question (old Chinese writing has no punctuation marks).
Su means to revive, to come to, or to rise again.
Just like people speak English with different accents in different parts of America, most Chinese don't speak 100% Beijing Mandarin. Their speech has a hint of their particular accent. Many Chinese pronounce Ye1 Su1 as Ye2 Su1. In that pronunciation, the name Ye Su not only sounds close to the Latin pronunciation of Jesus, but also has a great meaning: Father who has risen again.
Kuai le is happiness, joy, delight, or rejoicing.
Thus, Ye Dan Kuai Le, or Jesus' Birth Happy, is how you say Merry Christmas in Chinese.
