I think the implication of calling someone 'reserved' is that he or she is avoiding talking about things that they could speak about, if they wished to. It can either be in the sense of not wishing to speak to others or even in deliberately keeping something from others.

This seems to be what Edward reacts to, although it is not necessarily what Marianne meant. The way she is using the word, I would take it to be the opposite of 'frank' or 'open', both of which are qualities Marianne admires. When they first meet Willoughby, one of their earliest impressions of him is "To the perfect good-breeding of the gentleman, he united frankness and vivacity".

And just after this, in the same chapter (10), Marianne says this of herself, in response to Elinor's teasing about how well the first visit with Willoughby went: "I have been too much at my ease, too happy, too frank. I have erred against every common-place notion of decorum! I have been open and sincere where I ought to have been reserved, spiritless, dull, and deceitful."

The word 'deceitful' there suggests that Marianne also believes that being 'reserved' means that you are not showing your true feelings, for whatever reason.

When Edward gets upset at the part you mention, Elinor clarifies for him: "Do not you know my sister well enough to understand what she means? Do not you know that she calls every one reserved who does not talk as fast, and admire what she admires as rapturously as herself?"

But, as we later find out in this week's reading, it might be Edward's guilty conscience that causes him to imagine that 'reserved' means he is deliberately keeping something from them:

Edward stared -- "Reserved! Am I reserved, Marianne?"

"Yes, very."

"I do not understand you," replied he, colouring. "Reserved! -- how, in what manner? What am I to tell you? What can you suppose?"

I think he's wondering if they have learned or guessed his secret about Lucy, and if Marianne is admonishing him for this.