Quote 1
She let her mind dwell on the quiet vestibules, hung with Oriental tapestries, lighted by tall lamps of bronze, and on the two tall footmen in knee breeches who dozed in the large armchairs, made drowsy by the heat of the furnace. She let her mind dwell on the large parlors, decked with old silk, with their delicate furniture, supporting precious bric-a-brac, and on the coquettish little rooms, perfumed, prepared for the five o'clock chat with the most intimate friends, men well known and sought after, whose attentions all women envied and desired. (3)
Mathilde spends her time living in a dream world, in which she imagines all the fabulous things she'd have if she were rich. The most detail we get in the otherwise sparse story comes in Maupassant's descriptions of the fancy stuff Mathilde wants. But being rich also means more than just nice stuff to her: it means having the glamour to attract men.
Quote 2
She had a rich friend, a comrade of her convent days, whom she did not want to go and see any more, so much did she suffer as she came away. (6)
Mathilde wants to be wealthy so badly that she's driven mad with jealousy by the one rich friend she has, Mme. Forestier. She can't bear to see Mme. Forestier, because it brings her within arm's reach of the world of wealth she wants so badly, but can't have.
Quote 3
She reflected a few seconds, going over her calculations, and thinking also of the sum which she might ask without meeting an immediate refusal and a frightened exclamation from the frugal clerk. (24)
It looks like Mathilde is milking her husband for all he's worth here. Was her the crying fit put on so she could seize the opportunity to get a fancy dress from him?