Is Solaris even a character? Should a planet/brain/god/whatever be considered a person?
This is kind of the big unanswered question at the heart of Solaris. Is the alien a human? How can you even tell? Snow suggests that seeing the planet as a character is myopic or insular: "We are only seeking Man. We have no need of other worlds. We need mirrors. We don't know what to do with other worlds" (6.90). Okay, so we shouldn't think of it as a person.
But then what? It seems to do stuff, after all, and it definitely sends out the visitors. Are they there to say hello? Are they testing the scientists? Is Lem testing us? Gah. Our heads hurt.
Maybe you could think of Solaris as a character defined by not being a character. We don't know its motives. We don't know what it wants. We don't know what it thinks. We don't know what it feels (even though Kelvin's dissertation was about that very subject). And we definitely don't know whether it's a god or a monster or a human or just a big old lump of liquid. It's a mystery, like other worlds—or other people.
For more on this planet, be sure to check out the "What's Up With the Title?" and "Setting" sections. As for what a freaking mystery it is as a character, well, we recommend you read other characters' analyses elsewhere in this section. You just might notice a trend.