Someone asked this question on another post and I answered it in the comments section but I think it's such a great question so I'm posting it here.
Q: Why was leaving mitzrayim called the geulah if we only ended up in the midbar?
A: You are asking a really good question! I never thought of that!
The Jews left mitzrayim which was a place of real slavery. While they were there, they had to do backbreaking labor. The men had to do jobs that were cut out for women and the women had to do work that men usually do! That's how mean they were to the Jews!!
So yes, they left a place of intense slavery - that's why it is called geula! They became free people when they got the Torah, which was one of the goals of yetzias mitzrayim. It says "ein lecha ben chorin ela mi she'oseik b'Torah" Why is someone who follows the Torah considered a free person? It's because true freedom is when one is a ruler over his temptations and can win over his innermost desires and make the right decisions. The Torah helps each person do that! It is a guide to help us overcome obstacles the yetzer hara puts us in and it helps us live the best and happiest life ever!!
Also, the Jews left mitzrayim and traveled through the midbar but that was just a pathway to get them to live in Eretz Yisroel. Once they were in the holiest land, they were able to build the Bais Hamikdosh and be SO close to Hashem! THAT is what true geula means!
May we all be zoche to that day really soon!!