A broad question with an even broader scientific literature speaking to it; I'll highlight a few of the major "camps" with key references that you can follow up with if you find them interesting:
Without any particular theoretical allegiance, Baumeister & Leary (1995) argue that the need to belong is a fundamental human motivation. You can read a bit more about what they argue this classification implies in my answer to another question here. Baumeister (1991) also describes belong alongside other core "meanings" of life in his book (which I found an interesting read).
Supporters of an attachment theory perspective (e.g., Mikulincer & Shaver, 2007a) argue that establishing a sense of relational security--the feeling that others can and will be there for you in times of need, and are generally well-intentioned--corresponds to better emotion regulation, social relationships, and more pro-social behavior (see Mikulincer & Shaver, 2007b, for a review).
From an existential psychology perspective (see Solomon et al., 1999), humans have a unique awareness of their inevitable mortality, which they respond to in a number of ways in an attempt to preserve their symbolic selves (Burke et al., 2010). Close relationships are theorized to serve as one of these sources of existential security (see Hart et al., 2005), and existential security in turn has been linked to health (Goldenberg & Arndt, 2008) and interpersonal relationships (Greenberg et al., 1990).
According to self-determination theory (see Ryan & Deci, 2000), relatedness is one of three core human needs. When these basic needs (the others include competence and autonomy) are met, people are more intrinsically motivated, and experience benefits to their mental health, and well-being, as well as in many applied areas (e.g., work, education, etc.,).
Finally, according to some clinical perspectives (e.g., Rogers, 1992), clients need to feel unconditional positive regard from their therapists in order for therapy to be successful.
Baumeister, R. F. (1991). Meanings of life. New York, NY: Guilford Press.
Baumeister, R. F., & Leary, M. R. (1995). The need to belong: desire for interpersonal attachments as a fundamental human motivation. Psychological Bulletin, 117(3), 497-527.
Burke, B. L., Martens, A., & Faucher, E. H. (2010). Two decades of terror management theory: A meta-analysis of mortality salience research. Personality and Social Psychology Review, 14(2), 155-195.
Goldenberg, J. L., & Arndt, J. (2008). The implications of death for health: A terror management health model for behavioral health promotion. Psychological Review, 115(4), 1032-1053.
Greenberg, J., Pyszczynski, T., Solomon, S., Rosenblatt, A., Veeder, M., Kirkland, S., & Lyon, D. (1990). Evidence for terror management theory II: The effects of mortality salience on reactions to those who threaten or bolster the cultural worldview. Journal of Personality and Social Psychology, 58(2), 308-318.
Hart, J., Shaver, P. R., & Goldenberg, J. L. (2005). Attachment, self-esteem, worldviews, and terror management: evidence for a tripartite security system. Journal of Personality and Social Psychology, 88(6), 999-1013.
Mikulincer, M., & Shaver, P. R. (2007a). Attachment in adulthood: Structure, dynamics, and change. New York, NY: Guilford Press.
Mikulincer, M., & Shaver, P. R. (2007). Boosting attachment security to promote mental health, prosocial values, and inter-group tolerance. Psychological Inquiry, 18(3), 139-156.
Rogers, C. R. (1992). The necessary and sufficient conditions of therapeutic personality change. Journal of Consulting and Clinical Psychology, 60(6), 827-832.
Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68-78.
Solomon, S., Greenberg, J., & Pyszczynski, T. (1991). A terror management theory of social behavior: The psychological functions of self-esteem and cultural worldviews. In Advances in experimental social psychology (Vol. 24, pp. 93-159). Academic Press.