We are not born alone. We are with our mothers at the very least. Often many others are there as well. Similarly, many people die with loved ones surrounding them. And in between, we are mostly dependent on the cooperation of others for anything we want to accomplish.
In order to do almost anything you can think of, you need the cooperation of other humans. Humans have evolved to cooperate, because cooperation gives us greater survivability. The bigger the organization, the more likely it will survive over the long term. But organizations depend on the cooperating humans who comprise them.
As a side note, this makes me think that organizations are a new form of being. Maybe the US Supreme Court wasn't that far off. Perhaps just as the bacteria in us that we are dependent on for our lives have no idea what we are thinking, businesses will be dependent on humans as component parts, but the component parts will have no idea they are part of something greater, with its own purposes.
Anyway, whether farming, hunting, making computers or creating a play, it goes much better when you cooperate with other humans, and some things, like the play, may not be able to happen at all without cooperation from others, whether they are fellow players or the audience.
It's pretty simple, really. Humans need each other. Humans that cooperate are better off than other humans. Their children will be more likely to survive and pass their genes on.
That's on the practical level. The evolutionary level. But perhaps you were asking about the more mystical and existential component of human relationships -- things like love and companionship. Do we need anyone who knows us intimately? Who can share our thoughts? Live closely with us?
Well, it's hard to separate this from the evolutionary argument. The social and spiritual stuff helps us cooperate with each other, and you could argue that the function of love is to foster human cooperation. The reason we feel good when we have love is to encourage us to love, because people who love do better at passing their genes on.
So in the end, human relationships are important because the greater our cooperation, the more likely our genes will survive to reproduce and reproduce to survive. All the stuff about love and meaning may be something we like to agonize over, but in the end, it's not in charge. Our genes are in charge.