Apple: What is the difference between “/private/var/vm” and “/vm”?
/var/vm/sleepimage is used to store the contents of the RAM during hibernation, and the hybrid hibernation and sleep mode that Mac laptops use by default. If you have 8 GiB of RAM, /var/vm/sleepimage takes about 8 GiB of disk space. I don’t know why it isn’t deleted after waking up from sleep though.