The Moon is the heart of the natal chart. When a person needs security, they turn inward to its familiar, intimate energy. It represents childhood and mother. Its element is water. Any feelings (or lack thereof) in love relationships will be decided by the condition of the natal Moon.
Uranus in the natal chart is responsible for upheaval. Its energy comes from a distant place, blasting away the things that need to be changed. It represents anything new, innovative or shocking. Its element is air. It is the universal alarm clock.
Anytime the Moon makes an aspect to Uranus in the natal chart, the emotional and the detached are combined. A good illustration of this is the moment of birth: the infant is yanked from its safe, watery environment and feels the awakening slap of cold air. What does this mean for the Moon-Uranus person in a relationship?
It helps to understand where the Moon-Uranus person is coming from. The Moon in any hard aspect (conjunction, opposition, square) to Uranus can indicate a traumatic event in childhood where security was ripped away. A quick word about aspects: I am focusing on hard aspects because they indicate trauma more than the harmonious trines and sextiles. Although all Moon-Uranus aspects will have a similar theme, the way the energies interact will vary according to the aspect. In a square, the two planets are butting heads. The opposition has the two planets at opposite ends of a table shouting at each other. The conjunction is the two in an uneasy dance where both partners try to lead.