The importance of Mrs. Bennet's requesting, in chapter 1 of Pride and Prejudice, that her husband visit the young man (Mr. Bingley) has to do with propriety and courtesy. These were highly held values both in the era in which the novel was published (1813) and in the time period in which it was set (likely the late eighteenth century). It would never do Mrs. Bennet and her daughters (one of whom she wished to marry off to the newcomer Mr. Bingley) to descend upon their new neighbor without a prior acquaintance and appropriate introduction. Accordingly, as Mr. Bennet would have been the understood and undisputed head of the Bennet household, it was his duty, in the eyes of both society and his wife, to meet Mr. Bingley first, both to ascertain what sort of man he was (whether truly desirable for marriage to a Bennet daughter or not) and to pave the way for Mrs. Bennet and her daughters to meet him.
That Mr. Bennet is so contrary to his wife's request, and that she is so very insistent upon the point through their conversation in chapter 1, is almost an ironic commentary on the standards and requirements (most of them unspoken but all of them universally understood, accepted, and abided by) of the day. Mr. Bennet "see[s] no occasion" for his visiting Mr. Bingley, contrary to the standards of society, in which he would both know his duty and do it whole-heartedly without his wife having to browbeat him into it first. His wife insists that "it will be impossible for us [meaning herself and her eligible daughters] to visit him [Mr. Bingley] if you do not," as she is all too aware of the sense of propriety her husband should hold. She is determined to force him to do his duty, if for no other reason than the fact that, in that society, women could not exactly make the acquaintance of just anybody.