Joseph's family was called Israelites or Hebrews. (Remember, Jacob's 12 sons made up the different tribes of Israel.) They moved to Egypt during the famine after Joseph had saved food during the years of plenty. The Israelites had children and then their children had children. Soon there were a lot of Israelites living in Egypt.
A new king who was called Pharaoh came into power in Egypt. He didn't like it that there were so many Israelites and he thought they would one day take over the land. So he decided to make all the Israelites slaves. They had to work very hard and were not treated well by the Egyptian people. But Pharaoh was still worried about how many Israelites there were. The Israelites families were getting bigger so he decided to make a law to try and control the population. If any boys were born to the Israelites he would have them killed.
At this time there was an Israelite couple who was expecting a baby. When they had a baby boy (whose name would later be Moses) they decided to hide him, so he would not be killed. They hid Moses for three months, but as he got older it became harder to hide him. So his mother coated a basket to keep Moses safe and dry and placed him in the basket. She placed the basket in some tall grass, or reeds, in the Nile river.
Baby Moses had a sister named Miriam, and she watched from a distance to see what would happen to her baby brother. Pharaoh's daughter had come to the river for a swim. While she was swimming she noticed a basket floating in the river. She asked one of her servants to go get it.
Miriam had been watching, and she hurried over and asked, "Would you like me to go find an Israelite woman to feed the baby for you?" The Pharaoh's daughter agreed, so Miriam ran and told her mother that Pharaoh's daughter had found him and wanted someone to nurse him. When he was older, he went back to live in the palace with the Pharaoh's daughter. He was given the name Moses, which means "I drew him out of the water."
This entire story is one of faith and miracles.