The Israelite's enslavement in Egypt was not a punishment for some sin on their part. On the contrary, God originally brought the Israelites to Egypt to save them from a terrible famine. Joseph sums it up in Genesis 50:20: "But as for you, ye thought evil against me; but God meant it unto good, to bring to pass, as it is this day, to save much people alive." God allowed the Israelites to be enslaved so that He could bring glory to Himself by demonstrating His authority and power through miraculously delivering His people and keeping His promises to them.
One reason He allowed the Israelites to be enslaved in Egypt was to show His power and His ability to keep His covenants. We should first note that God told Abram that his descendants would face enslavement back in Genesis 15:13-14:
And he said unto Abram, Know of a surety that thy seed shall be a
stranger in a land that is not theirs, and shall serve them; and they
shall afflict them four hundred years; and also that nation, whom they
shall serve, will I judge: and afterward shall they come out with
great substance.
God did not mention to Abram or to anyone else that the Israelites' enslavement would be a result of sin. He only foretold that it would happen and that He would judge the nation that enslaved them and deliver them.
In Exodus 3:19-20 God tells Moses, "And I am sure that the king of Egypt will not let you go, no, not by a mighty hand. And I will stretch out my hand, and smite Egypt with all my wonders which I will do in the midst thereof: and after that he will let you go." Later in Exodus 7:3-5 God explains again:
And I will harden Pharaoh's heart, and multiply my signs and my
wonders in the land of Egypt. But Pharaoh shall not hearken unto you,
that I may lay my hand upon Egypt, and bring forth mine armies, and my
people the children of Israel, out of the land of Egypt by great
judgments. And the Egyptians shall know that I am the LORD, when I
stretch forth mine hand upon Egypt, and bring out the children of
Israel from among them.
God was using the terrible situation in Egypt to yet again work out something good to His glory. As we see later on, God continually refers to His mighty signs and wonders in Egypt to remind the Israelites of His power and integrity:
Exodus 20:2 - I am the LORD thy God, which have brought thee out of
the land of Egypt, out of the house of bondage.
Exodus 29:46 - And they shall know that I am the LORD their God, that
brought them forth out of the land of Egypt, that I may dwell among
them: I am the LORD their God.
Leviticus 26:13 - I am the LORD your God, which brought you forth out
of the land of Egypt, that ye should not be their bondmen; and I have
broken the bands of your yoke, and made you go upright.
Deuteronomy 5:6 - I am the LORD thy God, which brought thee out of the
land of Egypt, from the house of bondage.
Judges 2:1 - And an angel of the LORD came up from Gilgal to Bochim,
and said, I made you to go up out of Egypt, and have brought you unto
the land which I sware unto your fathers; and I said, I will never
break my covenant with you.
God makes it clear that He intended for the miraculous deliverance from Egypt to be a great display of His power and a constant reminder of His integrity for His people. Although the Israelites were stubborn and stiff-necked, they still remembered and honored God and praised Him for His mighty deliverance regularly through the Passover feast. In the book of Joshua, we see that other nations also remembered the events of the Exodus and knew of God's power. When the Israelite spies went into Jericho, Rahab told them in Joshua 1:9-10 how her people were afraid of the Israelites because of what they knew God had done for them:
And she said unto the men, I know that the LORD hath given you the
land, and that your terror is fallen upon us, and that all the
inhabitants of the land faint because of you. For we have heard how
the LORD dried up the water of the Red sea for you, when ye came out
of Egypt; and what ye did unto the two kings of the Amorites, that
were on the other side Jordan, Sihon and Og, whom ye utterly
destroyed.
God used the Israelites' enslavement in Egypt as an opportunity to demonstrate His power and integrity to His own people and to all who would oppose them. The miracles God used to deliver the Israelites served as reminders of Who was on their side and helped pave the way for their future conquests by showing their enemies Who they were dealing with.
The Israelites' enslavement also served as prophetic foreshadowing. As we know, Jesus also lived in Egypt for a time. Matthew 2:13-15 says,
And when they were departed, behold, the angel of the Lord appeareth
to Joseph in a dream, saying, Arise, and take the young child and his
mother, and flee into Egypt, and be thou there until I bring thee
word: for Herod will seek the young child to destroy him. When he
arose, he took the young child and his mother by night, and departed
into Egypt: and was there until the death of Herod: that it might be
fulfilled which was spoken of the Lord by the prophet, saying, Out of
Egypt have I called my son.
Matthew was, of course, referring to Hosea 11:1, in which God says, "When Israel was a child, then I loved him, and called my son out of Egypt." God also called Israel His firstborn son in Exodus 4:22:"And thou shalt say unto Pharaoh, Thus saith the LORD, Israel is my son, even my firstborn." Matthew 2:15 shows us that Hosea 11:1 is not only a retelling of historical events but also a prophecy of Christ's exit from Egypt. Joseph brought God's firstborn son Israel into Egypt to save it from a famine. Joseph, Jesus' earthly father, brought God's only begotten Son into Egypt to protect Him from Herod. Prophecy can't get more spot-on than that! This prophecy and its fulfillment serves as one of a plethora of prophecies identifying and confirming Christ as the promised Messiah. The narrative of Israel's enslavement and deliverance is also closely tied to the Passover lamb as a picture of Christ, which is another deep study all on its own.