As a result of his rebellion, Korach is swallowed up by the ground, to remain there indefinitely, chanting ‘Moshe emes ve’Toraso emes.’
It is a basic principle that all punishments are midah ke’negged midah; the punishment matches the crime perfectly. So how was the earth-swallowing punishment connected to Korach’s rebellion then? One approach is that Korach was challenging the ‘natural order’ of Klal Yisrael.
In claiming that Bnei Yisrael were too holy to need leaders, Korach was essentially destroying the carefully-assembled fabric and structure of Bnei Yisrael. Thus, since Korach was destroying our natural order, the world’s natural order (represented by the stiffly reliable ground) was turned upside down to punish him.
This also explains the connection to the next part of the sedra – the various presents given to Kohannim and Leviim – for these are the halachic framework of the structure of Klal Yisrael that Korach was seeking to destroy.