The next books fill in the pieces of Salander's past for the readers and, perhaps, some of the meaning behind her tattoo. We do have some clues. After Salander is raped by Nils Bjurman she goes to a tattoo shop and has "a simple little […] narrow band […] put on her ankle" (14.12).
When the tattoo guy asks her if she's certain she wants another tattoo, she says, "It's a reminder" (14.16). We can easily decode the symbolism here. Bjurman put a band around her ankle (and her other ankle, and her wrists) when he imprisoned her. This tattoo band is a reminder to never let anybody get hold of her that way again.
Likely, there's similar symbolic meaning to the other tattoos as well. They might just be a map of her past, on her body. OK, so she has the dragon, a rose, "a Chinese symbol" (11.2), a wasp, a band along the other ankle, and a band around her bicep. The wasp refers to her hacker name. Maybe the other ankle band refers to her stay in the psychiatric ward, another time she was restrained.
We don't know if Salander's dragon breathes fire, but the second book suggests that it might. As maddening as it is, this book also doesn't tell us what the rose, the Chinese symbol, or the band around her bicep symbolize. All the more incentive to read the other books! And, when you do, watch out for the way the tattoo map on Salander's body changes as she does.