“Blessed are the pure in heart, for they will see God.” People who are pure in heart believe God, and thus will be saved, which is why Jesus said they would see God. In the future God will indeed live with His people (Rev. 21:3). That the pure in heart would be saved and live forever, and thus get to see God, was a common teaching in the Old Testament.
In this context, the word “see” would include not only seeing God, but understanding Him better. Isaiah 11:9 says, “the earth will be full of the knowledge of Yahweh like the waters cover the sea” (cp. Hab. 2:14). In the future, the people who are saved will physically see God and also know Him.