P&P is essentially a feminist social commentary of the late 18th-early 19th century which Austen lived in. During that era women's roles were limited, having little of the independence that the modern women enjoy. Instead, they often had to resort to marriage in order to advance themselves socially or even just survive.
'It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife' is related to this idea. What Austen is saying isn't really that all wealthy bachelors are in need of a wife, but that women always assume a wealthy, single man to need a wife- i.e. themselves, or their daughters. It is, as other replies have mentioned, a jibe at Mrs Bennet who consistently strives to get her daughters married, but also a jibe at society in general.
In the context of the novel this quote is significant, because Elizabeth (the female protagonist) as well as her sisters are representative of the dependent young women who MUST marry well in order to remain respectable, or even to progress upwards on the social ladder. The quote therefore is also a confirmation of Austen's belief that women in her society were very much dependent on marriage and this has progressed to such an extent that women have thus ended up looking upon all wealthy bachelors as prey. Hence, the assumption that "all wealthy bachelors MUST be wanting to get married" actually disguises the truth, that it is in fact the women who are desperate for marriage.
There's really not much else to say on this, because it's a quote that's been examined and beaten to death by so many critics. As for why it's so famous, well, it's probably because it's a very insightful comment regarding society during Austen's time.