Laura Fairlie is so passive that she nearly disappears from view. Even Walter recognizes that Laura has a sort of dim, blurry aura hanging around her:
A fair, delicate girl, in a pretty light dress, trifling with the leaves of a sketch-book, while she looks up from it with truthful, innocent blue eyes […] The woman who first gives life, light, and form to our shadowy conceptions of beauty, fills a void in our spiritual nature [...]. (22.214.171.124)
Laura's looks reflect her behavior. She rarely acts for herself, and she doesn't speak much. Her passiveness is further emphasized by her lack of a narrative—she's one of the few characters who never tells her own story in her own words; she always speaks through Walter or Marian.
While Laura is passive in terms of action, she's not in terms of emotional displays. She spends the majority of the book in tears or having some sort of emotional meltdown. She's upset over Walter, she's upset when she marries Sir Percival, she's upset during her horrible marriage, she's really upset when Marian is sick, and she has a nice case of post-traumatic stress syndrome after getting out of the asylum.
Okay, we're just going to say it: Laura is just a perpetual victim/basketcase.
And yet Laura is loved by a lot of characters—Walter, Marian, Mr. Gilmore. So what is the attraction here? In a lot of ways she's just a stereotype: a damsel in distress.
Laura is described as very sweet and nice. She's likable in her own way, and her negative character traits potentially have some weight and reason behind them. See, Laura provides us with some good social commentary on the condition of women in this period. Wilkie Collins was a bit of an early feminist, and his major pet peeve was how horribly the institution of marriage treated women. By making Laura weak and helpless, he really hammered home just how dangerous and damaging marriage could be for women:
"I can never claim my release from my engagement," she went on. "Whatever way it ends, it must end wretchedly for me. All I can do, Marian, is not add to the remembrance that I have broken my promise and forgotten my father's dying words, to make that wretchedness worse." (126.96.36.199)
Pro-tip: any time you find yourself using the word "wretched" twice in the same breath, you're in a really nasty pickle of a situation. Run, don't walk, from the doubly "wretched" engagement.
Laura's initial, and almost inexplicable, refusal to say "no" to Percival can also be seen as a form of social commentary on the conditioning of women by the paternalist attitudes of the day. In other words, Laura is totally under the control of the men in her life; her ability to act of her own will has been seriously robbed.
Of course, social commentary sounds nice and all, but the truth is that Laura can be a pain. Her stubborn passivity can really be seen as a convenient way to move the plot forward.
Regardless of how you view Laura's passivity, it's one of the most defining aspects of her character.
One of Laura's other major character traits is the fact that she's traumatized. Laura spends a good chunk of the novel mentally unhinged (ironically enough) after being forced into an insane asylum. In a plotline that's a sort of a crescendo of the book's theme of identity, Laura is literally replaced with another person, Anne Catherick.
In the eyes of the world, Laura is dead, and after the trauma of the asylum, Laura's own sense of self is largely wiped out. This means that her sister and Walter have to take it upon themselves to heal her:
We helped her mind slowly by this simple means; we took her out between us to walk, on fine days, in a quiet old City square, near at hand, where nothing could confuse or alarm her […] we amused her in the evenings with children's games at cards […].(188.8.131.52)
But Laura's pre-asylum personality (or lack thereof) complicates matters. Laura is described as almost "childlike" in her helplessness after she's freed from the asylum. But Laura was depicted as childlike before her stay in the loony bin:
[S]he went on, twining and twisting my hair with that childish restlessness in her fingers, which poor Mrs. Vesey still tries so patiently and so vainly to cure her of. (184.108.40.206)
The comparisons of Laura to a child—in terms of appearance, behavior, and even intellect—start verging into Creepytown. Walter and Marian often profess their love for Laura, but there's a huge amount of protectiveness and pity mixed in to their feelings.
I raised her head, and smoothed away the tangled hair that fell over her face, and kissed her—my poor, faded flower! my lost, afflicted sister! (220.127.116.11)
Pity-party, table for two! And we're not touching Walter's "sister" comment with a ten-foot pole. (Although referring to your true love as a brother or sister wasn't uncommon in Victorian novels—Dickens's works have examples of this weirdness.)
If you tweak those feelings just a bit, and emphasize the pity a bit more, you get Walter and Marian's views on Anne Catherick, Laura's ill-fated doppelgänger. Check out Anne Catherick's character guide for more on that weird relationship—Laura ends up becoming Anne in a lot of ways after Fosco declares her to be Anne.
Names and the recognition of others are powerful things in forming a person's identity, and it's perhaps this theme that gets at the heart of Laura's character. Laura is always a reflection of the world around her, be it the restrictive society Victorian women lived in, the sinister machinations of Fosco, or the coddling of Walter and Marian.