In this context a "sliver" is a very narrow opening. The door has been opened just enoiugh to see out with one eye, perhaps. Indeed "sliver" here is a bit redundant with "cracked", but the redundancy emphasizes the narrowness of the opening
In other contexts a sliver is a thin or narrow slice or section of something. "A sliver of cake" is the thinnest possible slice of cake. "A sliver of wood" is a very thin piece of wood, probably too small to do much of anything with.
"Sliver" can also be used as a verb, meaning "to split or cut off (a sliver)", "to split or cut into slivers", or "to split"
As a comment notes, "cracked" in the original sentence could have been rendered as 'cracked open" which might have been clearer, but this sort of elision is very common, and would be understood by any fluent speaker.
See dictionary definitions: