Tajweed Means: To recite every letter correctly, from its makharij, with all its qualities.
Allah almighty states in Quran:

"And recite the Quran with measures"
In the commentary of this verse, Hazrat Ali (Radhiyallahu 'Anhu) states: "Tarteel means to know the tajweed of the letters and to recognize the places of pausing."

In a Hidth it has beeb narated that: "Allah desires that the Quran be recited in the manner it was revealed."
Since it is revealed with tajweed; it is compulsory to recite the Quran with tajweed.