Purification is more than wearing neat clothes or looking tidy. In Islamic practice it is connected with worship, bodily cleanliness, and the required rules of ritual purity. Wudu, ghusl, and avoidance of impurity are practical examples.
The vivid expression شَطْرُ الْإِيمَانِ establishes the great importance of purification. It does not calculate an individual’s percentage of faith or make other religious responsibilities unnecessary.
Remaining clean, observing rules of purity, and preparing properly for worship show serious attention to one’s obligations.