As I mentioned in the brief History of the Exodus, G-d spoke to Moses and told him of the impending Exodus. G-d said to Moses:

Therefore tell the Children of Israel that I am G-d, and I will take you away from the
oppression of Egypt, I will free you from their slavery, and I will liberate you with an outstretched arm (i.e. a demonstration of My power) and great judgments. I will claim you for me as a people, and I will be your G-d. You will know that I am Hashem your G-d who is bringing you out of the oppression of Egypt. I will bring you to the land I have sworn to give to Abraham, Isaac, and Jacob, and I will give it to you as an inheritance. I am G-d.

— Exodus 6:6-8

Five expressions of redemption are used here. These expressions correspond to the promises that G-d made to Abraham at the Covenant Between the Parts. G-d told Abraham that his descendants would be 1) aliens, 2) enslaved, 3) oppressed, 4) rescued to become the Chosen People, and 5) given the Land of Israel permanently.

The first act of Redemption that G-d did for us in Egypt was to stop the oppression. Therefore, the First Cup commemorates «I will take you away from the oppression.»

The second act of Redemption that G-d did for us in Egypt was to end the slavery. Therefore, the Second Cup commemorates «I will free you from their slavery.»

The third act of Redemption that G-d did for us in Egypt was to rescue us from Egypt with many miracles. Therefore, the Third Cup commemorates «I will liberate you with an outstretched arm.»

The fourth act of Redemption that G-d did for us was to bring us to Mount Sinai, give us the Holy Torah, and thus declare us his Chosen People. Therefore, the Fourth Cup commemorates «I will claim you for me as a people, and I will be your G-d.»

The fifth act of Redemption was to bring us to the Land of Israel. Unfortunately, that was not expected to be permanent, and indeed has not been. Even now, when many Jews live in Israel, it is not the kingdom that G-d has promised us. When the Messiah comes, we will institute the drinking of the Fifth Cup, to commemorate «And I will bring them to the land.»

We pray daily that the Messiah arrives soon. Thus many people, near the end of the Seder, have the custom to fill one extra cup, and place it somewhere prominent on the table. This symbolizes our hope that we will soon be permitted to drink a Fifth Cup.

The Prophet Malachi tells us that G-d will send us the Prophet Elijah before the Final
Redemption, to prepare us (Malachi 3:23). For this reason we call this cup of hopefulness the «Cup of Elijah.»

Simply drinking four cups of wine is not permissible. One cannot fulfill the requirement in that manner. One must drink the Four Cups at the appropriate times, interspersed between the various sections of the Seder.