The Israelites’ bondage in Egypt is described in Exodus chapter 1, particularly in verses 11-14. Essentially, when the Israelites began to multiply and become more numerous, the Egyptians made them into slaves. They did this because they were afraid that the Israelites would become too powerful, join with their enemies, and overtake them. To avoid this possibility, the Egyptians exerted their power over the Israelites first.
As slaves, the Israelites were put to work in building store cities for Pharaoh, working with bricks and mortar, and also working in the fields. They were greatly oppressed by the Egyptians but continued to grow in numbers. This worried the Egyptians even more, so they increased their oppression, even trying to kill infant boys. An example of this is found in Exodus 1:15-22, and leads to the birth and preservation of Moses in chapter 2.
During their oppression, it is evident that the Israelites did not forget their God. Exodus 2:24 says that God heard the Israelites’ groaning, indicating that they had been pleading with God to deliver them. Exodus 1:21 also gives an example of the two midwives who feared God during their bondage and were rewarded for it.
Some may question why the Lord would permit such oppression to His people. The Bible does not say directly. However, there are many instances where God’s deliverance of their bondage was used to glorify God and to increase the faith of the Jews (and, in time, Christians).
Additionally, the experience of bondage and deliverance can be used as picture of the much bigger and more widespread bondage of mankind in sin. When Adam sinned, he and all his descendants were sentenced to death. They were separated from God in the garden of Eden and became trapped under the curse (Genesis 3). Thus, mankind — under the penalty of death — can be considered in bondage. However, with Jesus’ great sacrifice on the cross, he opened up the opportunity for mankind to be free from this bondage. By paying the ransom price of a perfect man (Adam) for a perfect man (Jesus), Jesus delivered mankind out of the bondage of sin and death and guaranteed a resurrection to all (1 Corinthians 15:20-22).
In summary: The Israelite experience in Egyptian bondage and their subsequent deliverance illustrates the much greater bondage of mankind and the even more glorifying deliverance that will occur as a result of our Lord Jesus’ sacrifice.