Jane Austen uses the word 'taste' more than two dozen times in the novel, and about half of these are in this opening section.

I'll come back to this point later in the novel as some of the later references play into this, but I think the concept of what constituted 'taste' has a lot to do with Marianne's own particular brand of sensibility.

There were not only things one ought to have strong feelings about, such as literature, music or drawing, but more particularly, there were correct and incorrect things to admire, in her opinion.

The variety of nuances to the idea of 'taste' is interesting, I think.

Marianne confides to her mother in Ch. 3 that she is afraid Edward:

has no real taste. Music seems scarcely to attract him, and though he admires Elinor's drawings very much, it is not the admiration of a person who can understand their worth. It is evident, in spite of his frequent attention to her while she draws, that in fact he knows nothing of the matter. He admires as a lover, not as a connoisseur.

Marianne is convinced she could never be happy with "a man whose taste did not in every point coincide with [her] own."

It seems, from these statements, that she believes there is a kind of 'proper' taste which must be cultivated and educated, and that to admire anything else or to admire something just because you like it is a sentiment of lesser value.

In Ch. 4, Marianne even tells Elinor that it's a pity Edward "has no taste for drawing".

Elinor feels compelled to defend him by explaining that he enjoys looking at other peoples' drawing and that he is "by no means deficient in natural taste" and that "he has an innate propriety and simplicity of taste."

Marianne doesn't want to hurt Elinor's feelings and agrees that Edward has goodness and sense, but in her view, only "rapturous delight" can truly be called 'taste' and Edward does not demonstrate that.

Yet we learn from Elinor that (probably because he feels more at ease with her and they spend more time together) he does offer "his opinion on subjects of literature and taste;" and Elinor finds that "his observation just and correct, and his taste delicate and pure."

However, upon learning that Edward and Elinor are not actually engaged, Marianne declares that the (temporary) delay will give Edward "greater opportunity of improving that natural taste for [Elinor's] favourite pursuit (drawing), which must be so indispensably necessary to [Elinor's] future felicity."