When you are "double-minded" you simultaneously want two things at once. You might desire peace with God, but you also insist upon your "rights." Or you might attempt to do the right things for the wrong reasons: for the hope of reward, for pride, for patriotism, or for other motivations. Such double-mindedness can cause a divided focus, an astigmatic condition of spirit that results in half-hearted conviction and the dissolution of the will. Put the other way around, single-mindedness concentrates the will and produces wholeheartedness, conviction, and genuine character.
In the passage above, Moses commands us to be tamim (תָּמִים), i.e., "finished," "complete," or "perfect" before the LORD. Note that this Hebrew word does not denote ideal moral perfectionism as much as it suggests being "thoroughly made" or brought to successful completion. For example, tamim is used to describe completed years (Gen. 47:18); healthy animal sacrifices (Lev. 22:21-22); nourishing vines (Ezek. 15:5); truthful speech (Amos 5:10); finished building projects (1 Kings 6:22); and even the fulfilled destruction of a people (Num. 14:33). In our relationship with God, tamim means being wholehearted, resolute, and entirely committed to walking "with" Him in this world. This is what Jesus meant when He said, "Be ye perfect..." (Matt. 5:48).
People live in despair because they are often double-minded. Consciously or not, they are attempting to look at two different things at once. They seek their end in a world of finite things – in "good fortune," in personal honor, in worldly entertainment, or other immediacies of the passing day. Such a cross-eyed approach leads to disorientation and spiritual destruction. A divided house cannot stand.
The mature of heart, however, the "pure in heart," do not look away from the faithfulness and love of God. Despite the distractions of temporal testing and difficulties, they retain their commitment and their earthly decisions reflect their faith. All this turns on the decision to genuinely trust in God. As Jesus said, "if your eye is single, your whole body shall be full of light" (Matt. 6:22).