“Blessed are the pure in heart, because 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 (cp. Ps. 24:3-5; 73:1).

That the pure in heart will “see God” is literal, and mostly refers to seeing God in the future when the Lord returns. In the Millennial Kingdom saved people will see God like the apostles did, by seeing Him in His Son and representative, Jesus Christ, and in the Everlasting Kingdom they, all the saved, will see God face to face (Rev. 21:3). Here in the context of Matthew 5:8, 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.