If you are new to the Baha'i Faith, a good starting point is the Baha'i International Community site:
One of the clear statements found on that site is this:
"`Abdu'l-Bahá gave significant attention to delineating the administrative system conceived by Bahá'u'lláh, and in His Will and Testament specified the responsibilities and functions, powers and authority particularly of the two institutions that would succeed Him, thus providing for continuity in the unity of the Bahá'í Faith. The twin institutions at the apex of the administrative order are the Guardianship and the Universal House of Justice. "
The clarity of this statement is important, because it uses the term "successor" in connection with the Universal House of Justice. The House of Justice is not only the Head of the Baha'i Faith and its Supreme Body: It is part of the line of succession set forth by the Founder of the Baha'i Faith and by `Abdu'l-Baha. It expresses the same point made by Shoghi Effendi when he referred to "the Covenant the Master made with the Baha'is that they should accept His administration after Him." (From a letter on behalf of Shoghi Effendi dated Oct. 21, 1932; US Baha'i News #80, January 1934, pp. 5-6)
Often, when speaking about the Universal House of Justice Baha'is correctly point out that the Universal House of Justice is the Head of the Baha'i Faith. That's correct, as far as it goes. But, like Shoghi Effendi, it is also one of the twin successors to the Central Figures of our Faith. As Shoghi Effendi wrote:
"They [Baha'u'llah and Abdu'l-Baha] have also, in unequivocal and emphatic language, appointed those twin institutions of the House of Justice and of the Guardianship as their chosen Successors, destined to apply the principles, promulgate the laws, protect the institutions, adapt loyally and intelligently the Faith to the requirements of progressive society, and consummate the incorruptible inheritance which the Founders of the Faith have bequeathed to the world."
(Shoghi Effendi, The World Order of Baha'u'llah, p. 19)
The Universal House of Justice is a Successor to Baha'u'llah and `Abdu'l-Baha. That's an important concept for us to grasp.