The exact answer has not been revealed, but some conclusion can be drawn from different episodes and chapters of anime and manga.
The prelude of several episodes of Attack on Titan stated that:
Over a hundred years ago, humanity suddenly found itself faced with a new predator. They were more powerful than humans. Humanity was immediately pushed to the brink of extinction. The survivors built three walls: Maria, Rose, and Sina.
From the anime and manga:
- The Female Titan spared Armin's life several times.
- The walls were built with the exoskeletons of titans.
- Colossal Titan, Armored Titan, Female Titan (i.e. Bertolt Hoover, Reiner Braun, Annie Leonhart respectively) and other Titan Shifters actually lived among humans.
- Ymir turned into titan and protected her friends from other titans.
- Rich people and the top brass who mainly lived inside Wall Sina knew a lot about the titans, the walls and the titan inside the walls.
- The titans who broke through the wall and led other titans inside were mainly the Colossal Titan and Armored Titan, and their objective was to search for the mysterious power known as the "Coordinate".
These points lead me to conclude that their main intention is not to destroy humanity, but to find the Coordinate ability for which they may destroy humanity. The relation of the Titan Shifters with human, and their willingness to sacrifice their lives for their friends shows that their main intention was not to destroy humanity. And humans are not as weak as they seem to be; titans need to make some effort to destroy all humans, and those titans with brain know that.