What factors in westward expansion shaped the U.S. and British North American colonies? What caused people to want to expand?

The major factors that caused people to want to move west were economic and social.  These two types of factors were closely related.

Economically, people wanted more opportunities.  During this time, America was a mainly agrarian economy and the West had land that was free or very cheap.  By moving West, people could get a much better opportunity to prosper.

Socially, people wanted more freedom and autonomy.  Moving West was seen (especially in colonial days) as a way of getting away from the control of the upper classes.  So moving west was seen as a way of asserting independence.

Both of these helped influence people to move west.