The Triumphal Entry was something that would have been very common in Jesus' time.  The irony of Jesus' entry into Jerusalem is that it mirrored a common Roman practice also called a Triumphal Entry. 

We have a vision of freedom in our heads, that we can do whatever we want, but Jesus comes to offer a better kind of freedom.  Jesus subverts this Roman tradition, which would have offered a kind of freedom to specific people, and shows us that he is offering a different kind of freedom.  A spiritual freedom for all people.