I need to know the meaning of this sentence. Why do Americans walk with there heads down and there feet up.
Since you give American English as your native language, I'll assume you understand the meaning of the words (once you've interpreted "there" properly).
The discourse meaning seems to be that it's the first line of a joke or riddle. Does this accord with the context in which you found it?
When you understand the question, perhaps you could tell us the answer?
If you correct 'there' to 'their' in both cases, you will find that google is your friend.