Travel Document is a document to be used in travel. It is issued by your own government. Travel Document is not necessary a passport.
In Hong Kong, there are 4 types of travel documents:
http://www.immd.gov.hk/chtml/hktraveldoc.htm
You have to apply based on your status. Then afterward, you have to go the U.S. Consulate to apply a visa, which is an authorization to entry.
Travel Document itself can't allow you to go to the United States and study. However, with proper authorization (Student Visa), you can go to there.