As the guys say, foresee and predict are synonyms. Imagine the root meanings as being 'see before it happens' and 'say before it happens'. Therefore, a prediction is something that is said. To foresee something does not mean to say it, it can mean to act in a way that shows a knowledge of the future. Neither of these words have a magical connotation, because the knowledge comes from things that can be observed. Prophesy (or to prophesise) is to tell a story about the future, which you believe will come true. There is no observable reason for this story, so prophesy is somewhat magical. Most prophets (a person who prophesises) are considered either mad or magical, depending on whether their prophesy comes true :)

Foresee and predict are verbs. Prophesy is a noun. Predict is probably the most common one. Foresee is a bit more poetic.

你这问题里面最后一个词儿我都不认识，太高端啦~~~

"foresee" and "predict" are synonyms and are more or less equally common in everyday speech, in my experience. They are however both still formal words. "I predict that the weather will get worse later today" "I foresee that sales will return to normal levels soon" "Foresight" relates more to the imagination, whereas "prediction" relates more to the intellect, analysing evidence. prophesy" has a similar meaning but is less common in everyday speech; it sounds dramatic and so is more common in literary works: "He prophesied that the young boy would one day become a great leader."

This is an example of a prediction: "Jeremy Grantham's firm is predicting 5.6% annualized returns from emerging markets stocks over the next seven years." This is an example of foreseeing. Longer-range, less definite, more visionary. "On the one side, there are people like Aubrey De Grey ... who foresee great progress within a few decades after major funding is achieved. On the other, people [like David Brin] who look towards changing metabolism to slow aging, and who foresee little progress over the next few decades because the challenge of building a new, viable human metabolism is very, very hard." This is an example of a prophecy (from the Book of Daniel in the Old Testament): "Daniel answered in the presence of the king, and said... there is a God in heaven that revealeth secrets... Thy dream, and the visions of thy head upon thy bed, are these... Thou, O king, art a king of kings... And after thee shall arise another kingdom inferior to thee... And the fourth kingdom shall be strong as iron: forasmuch as iron breaketh in pieces and subdueth all things: and as iron that breaketh all these, shall it break in pieces and bruise. And whereas thou sawest the feet and toes, part of potters' clay, and part of iron, the kingdom shall be divided... And in the days of these kings shall the God of heaven set up a kingdom, which shall never be destroyed: and the kingdom shall not be left to other people, but it shall break in pieces and consume all these kingdoms, and it shall stand for ever."