This is a question which needs elaboration to describe exactly what you mean by 'relationship.' We are related to everyone and every thing in some way. For example, you might have a very fond relationship with your present home: or you might hate it. You might find your relationship with dogs, or cats, or pet mice to be one of enjoyment, or abhorrence. So, if you're talking about a human relationship with another person, and really mean someone with whom people are in a close and intimate relationship, why don't you say so.
Of course, relationships of this type are important. They show us how WE are. What we see in another person as good or bad - a value judgement of some kind - could well be a reflection of our own virtues or vices. As it has been said by such persons as Dr. Wayne Dyer, when we point out something good or not good in another it doesn't tell about the other person so much as reveals to them things about ourself. We show our character by how we behave not others.
For example, those who criticise others become known as those who criticise. I think you'll get my drift.
What is the importance of relationship in my life? It is very important, for I continually define myself as 'how I am at this time' by how I act and react in my relationships, whatever the objects of those relationship be: animal, mineral or vegestable - everthing and ever thing. With out relationships where would we be? I'd suggest...no longer of this world.