It's described as a slug-like mass of decaying tissue that consumes anything it comes into contact with, including other Necromorphs. The remains of a decaying human skull inside the mass could be seen by Altman and at other times a human face that appeared to be laughing at him.
The Creeper's all-consuming nature was likely based on the extraterrestrial Blob in Frank Darabont's eponymous 1988 film. In the movie, the alien Blob is a slow amorphous mass of an unknown matter that consumes/dissolves any organic being it touches, including humans.
The Creeper appears to be susceptible to fire seeing as it retreats when burned by the Hydrogen Torch found by Altman in the same corridor the creature first makes its appearance. It isn't known whether this could be enough to kill the Creeper as Altman didn't stay around long enough to find out.
Having no visible limbs to dismember it is unknown exactly how the Creeper is killed, whether from sheer trauma to its body or whether it can be killed at all.
In Chapter 62, Altman sees another Creeper on a security camera feed. This may indeed be the same one from Chapter 59 which could mean there was only one Creeper aboard the Platform.
It is possible that the Creeper could be a more violent version of the Corruption and could be part of the process when a Guardian is made. It is possible that the Corruption and the Creeper are the same thing, but the Creeper is the earlier form of the Corruption when it is aggressive and must obtain bodies in order to make Guardians.
One possibility for the creation of the Creeper is that it was a by-product of Doctor Guthe's experiment before the outbreak. In his experiment, he synthesized the Necromorph DNA into sheep cells, then chemically stimulated them to grow. Being that Guthe injected himself with the virus and started the outbreak, he never closed the incubator where he was experimenting on one of the specimens. This would allow for the escape of the genetically-engineered tissue, and the chemical assistance it received could account for its rampant growth and acidic properties. If this is true it means that the Creeper is the only existing one of its kind, that being the reason one was never seen in anything but the book.