The expression “pure in heart” refers to a person whose inner most thoughts, motivation and purpose are pure, clean, wholesome and good; this is the one who will see God. To see God is to believe in God, and even more basic, they believe God; such a person is blessed indeed.
The person who is not pure in heart will not see God, possibly because he would rather not see Him. The person who is not pure in heart is one whose inner motivations are not wholesome or good, but are more likely centered on self, gain and getting what they want at whatever cost; they are not blessed because there is little room in their lives for a relationship with Him.
Rather sad, isn’t it?