The Department of Justice has a nice guide on each section of the Charter, including section 28.
As @MichaelSeifert's comment says, section 15 did not come into effect until later to give government time to resolve possible conflicting laws. During this time, section 28 can still be used to ensure other Charter rights are enforced on a gender equal basis.
During the period from 1982 until April 1985, section 28 was the only Charter guarantee of sexual equality. It has been said that this may be the main effect of that section. There is to date limited jurisprudence on section 28.
It is also important to note that section 28 is for interpretation of the Charter, not other laws. It cannot be directly applied to other parts of the constitution, ordinary laws nor other actions of the government.
28 Notwithstanding anything in this Charter, the rights and freedoms referred to in it are guaranteed equally to male and female persons.
Equally, section 15 cannot be used to challenge other parts of the constitution, it can only be used against laws and actions at a lower level (Adler v Ontario (AG), [1996] 3 S.C.R. 609).
The DOJ guide also describes this section as "interpretive, confirmatory, and adjunctive", in other word, symbolic. Nothing wrong with this, laws, especially constitutional acts that are profoundly political, are often symbolic. It also helps to contextualize section 1 analysis that determines the extent of acceptable limitations on Charter rights.
Additionally, in my opinion, a very important historic reason is the Persons case.
Section 28 is reminiscent and affirmative of the results in the that case, which declared that "persons" in the Constitution included female persons. This is was not as obvious as we would think today, gender-neutral language on its face did not mean that the law was interpreted in a gender-neutral way. Not to mention, in French, masculine forms (the Charter uses chacun and "tout citoyen canadien" for example) are often used as the generic (nothing wrong with this since gender in French is grammatical). But the section affirms the generic value of the expressions for both sexes, similar to subsection 33(1) of the Interpretation Act or other places where you see things like "masculine forms/pronouns has been used only for convenience and the rules apply equally to women.".
The Supreme Court of Canada rejected women as "qualified persons" within the meaning of the Constitution for the purpose of appointing Senators; it was only because SCC was not Canada's final court at the time that the case succeeded in the British Privy Council.
Notwithstanding clause
As a compromise with the principle of parliamentary supremacy, section 33 of the Charter provides that
(1) Parliament or the legislature of a province may expressly declare in an Act of Parliament or of the legislature, as the case may be, that the Act or a provision thereof shall operate notwithstanding a provision included in section 2 or sections 7 to 15. [...]
The legislatures cannot use the notwithstanding clause on other sections, e.g. democratic rights (sections 3-5), mobility rights (section 6) or language rights (sections 16-23). Section 28 is also not subject to a notwithstanding declaration, as such, it may mean that a government action notwithstanding other sections of the Charter nonetheless cannot violate sexual equality (but this question remain unsettled).
This is one argument used to challenge the Quebec law on state secularism. The litigation is still ongoing, but the decision of the Superior Court of Quebec so far has disagreed with the preceding interpretation. The Superior Court deemed that once the legislature suspended the application of a Charter section, the rights in that section essentially are no longer guaranteed by the Charter and section 28 cannot be applied.
