The novel begins with Sir Walter with his nose in a book. It soon becomes obvious, however, that Sir Walter is no bookworm: the Baronetage is the only book he reads. And what is the Baronetage? It's actually called The Baronetage of England, (still published today under the title Debrett's Peerage and Baronetage, after its original editor, John Debrett). It's basically a reference book that catalogues those strange creatures, the British nobility.
Sir Walter's obsession with his own entry in the Baronetage – to the point of adding further details – is the equivalent of a minor celebrity who writes an incredibly in-depth Wikipedia entry for himself. The Baronetage symbolizes the position in society that Sir Walter holds; his desire to make his entry longer than it is shows that his opinion of his importance is greater than the official record makes it.
His liking for the book was once shared by Elizabeth, who also shares his obsession with rank, but she now avoids the book like the plague. The reason? The book puts her still-single status in black-and-white, and reminds her that so far she's failed in what society dictates is her main purpose in life: to marry someone else with an entry in that book, the more impressive the better. Elizabeth sees the Baronetage as a symbol of her own inadequacy, though she might equally well think of it as symbolizing a social order more interested in maintaining its dominance through marriage than in whether those marriages are happy or not.