To split the Confederacy. The Mississippi River divided the Confederacy in two, and the North hoped that by gaining control of the river, it could split the Confederacy and make it easier to defeat.
To free the slaves. Many in the North believed that the only way to end slavery was to defeat the Confederacy and free the slaves. By gaining control of the Mississippi River, the North could cut off the South's supply of food and supplies, and force it to surrender.