Ysera is one of five Dragon Aspects empowered by the Titans to watch over Azeroth after their departure. Ysera's domain is a little less mundane than the others. Earth? Nope. Life? Nope. Magic? Nope. The eternal dream that flows throughout all things and is bound to the wilds of Azeroth? Yep!
Besides her involvement with the Emerald Dream, Ysera is probably best known for her relationship to Cenarius. The Dreamer has been described as Cenarius' mother before, which has caused some confusion since Elune is supposed to be his mother. The explanation for that is simple, if you think in terms of Gods and Demigods and not us tiny mortals. Elune is a Goddess. One of the few full god(esse)s that we know of in Azeroth. While Elune apparently finds the time to have one night stands with stags now and then, she really does not belong in the mortal realm. Likewise, the demigods really cannot be in her realm. Malorne (Cenarius' father) and Ysera were... business partners, of sorts. Thus, due to The Dreamer's relationship with his pops, Cenarius' upbringing was likely influenced more heavily by Ysera than the Moon Goddess. You could say Ysera adopted him, I suppose.
Like Alexstrasza, Ysera dislikes violence and death. She prefers to pacify or banish her enemies than destroy them utterly. Of course, this doesn't mean Ysera can't be violent, she most certainly can. Probably the most notable example of this is during the War of the Ancients, shortly after Malorne's death at the hands of Archimonde. Upon Ysera's arrival, she utterly ravaged the Legion's forces to reach the White Stag's side.
At the end of the aforementioned war, Ysera was involved in the creation of the original World Tree. Though planted and grown by Alexstrasza, Ysera and Nozdormu were involved in its creation as well. Nozdormu made the tree timeless, and through the tree, the Night Elves as well. That timelessness was to be used by Malfurion Stormrage and all future druids to help Ysera's work in the Emerald Dream, tending to the wilds of Azeroth. Ysera bound the tree to the Emerald Dream, allowing all Druids free passage into the eternal dream.
Ysera very rarely leaves the Dream, especially now that the Nightmare has been seeping through. In those few times she's seen in the realm of mortals, in a mortal form, she is always dressed in shades of green. Green hood, green clothing, green jewelry, yadda yadda. Unlike the other aspects that have taken an active role among mortals, it doesn't appear that Ysera has any particular preference in what form she takes. Alexstrasza prefers to appear as a High Elf, Deathwing prefers being Human, Ysera seems as if she would take the form of a Night Elf but she generally takes whatever form is most appropriate for the situation.
Her eyes are almost always closed when she is actually seen, almost appearing to be partially asleep and still dreaming while speaking to you. On very, very rare occasions, she will open her eyes. This generally is a sign that she's feeling some very, very strong emotion, and only then finds you important enough to require her full attention.
Ysera's already rare appearances have become increasingly so as the Nightmare gains momentum within the Dream. What, precisely, the Nightmare is is fairly vague to us at the moment. Most likely, it is created by the Old Gods, but there is a possibility it is something more obscure like a new enemy, or quite literally the nightmares of living things, the fear and corruption taking hold after the recent wars. It's probably that first one, though.
A majority of the Green Dragonflight has fallen victim to the Nightmare, but there are some that remain. We don't know that Ysera herself has fallen to it, and our old buddy Itharius makes a return in Wrath of the Lich King.
It is partially confirmed that we at least see Ysera's physical Dragon form in Wrath as well, but that is subject to change and we don't really know what role she will play, if any.
As you can see, Ysera's existence has not been filled with quite as much clear, easy-to-witness drama as Alexstrasza's has been, but she is certainly not a boring character. The Queen of Dreams' biggest chapter seems to be this Nightmare storyline, and that is only beginning, more or less. It will be interesting to see what happens in Northrend, and where it will go from there.
Oh, by the way, when we see Ysera, that picture above will probably not be what she looks like. The few official images of the Aspects that we have are pretty early renditions of them, and all of the old stuff is very, very subject to change. I imagine that Ysera, nowadays, would be given a more sleek appearance (on paper, not necessarily in WoW). That's only a guess, though.
If you want more information on Ysera and the Emerald Dream, you'll get bits and pieces from The War of the Ancients trilogy. She makes brief appearances in other novels, but they aren't particularly revealing about her character. You may get more out of the RPG books as well, but a lot of that information becomes outdates as WoW progresses, as the loremasters fit the lore into an MMO-friendly form. Still, they're a very good resource for things not in the game yet. I'm not discouraging you from reading it, just brace yourself for changes to what you know. It's happened to me plenty already.