@Ceili,
At that time, Egypt was ruling most of the areas around what we today see as Israel and other areas.
The Jews were tribes - if I am right - and wondered in large groups where there was good land for their animals.
That was nothing unusual. Here comes how it is explained in the Biblical records. Exodus 1:8-14 (King James Version).
Famine in the Land of Canaan forced inhabitants to find food.
Josef, the son of Jacob, had been sold by his brothers and ended up in Egypt, where, through a series of spectacular events, he becoming second in command to Pharoah. When his brothers came from Canaan for food, Joseph instructed them to bring their father and settle in Egypt. Jacob and his family moved to Egypt and their help was soon requested in building two cities for Pharoah, Pitom and Ramsees. Initially, they were paid for their services, but with the death of all of the 12 sons of Jacob (Levi died last) the employment relationship slowly shifted into one of servitude. Because the tribe of Levi hadn't been involved in the employment relationship, they were not subjected to work, despite what popular film may show.
While the actual implementation of the slavery may have been gradual, the biblical record indicates that a new Pharaoh came to the throne who 'knew not Joseph' (or didn't want to know) and so enslaved the Israelites. The thinking and process is described in the first chapter of Exodus. It must be remembered that Moses was brought up in the household of Pharaoh for 40 years and so would have been quite familiar with how they thought or regarded the Israelites.