Nollning could be roughly translated as 'hazing' or 'initiation', almost always in the context of starting at university.
You'll often see groups of young adults wearing student overalls or fancy dress, who are asked to carry out certain tasks by older students.
Typically the idea is that these should be a fun and harmless way to get to know fellow students, with tasks like a scavenger hunt or singing a song. Over recent years however, there have also been many reports of nollning rituals being used to bully or humiliate students both at high schools (gymnasium) and universities (högskola/universitet). Alcohol usually plays a part in the activities too, but drinking and taking part in the tasks should in theory be totally optional.
The name nollning comes from the term nollor (literally 'zeroes') which is used to refer to the new intake of students. But although 'zeroing' might sound degrading, there's no negative connotation to nollor, which is the equivalent to 'fresher' or 'freshman' in English, and students become ettor (ones) once their first year of studies officially starts.
Note: Despite this, it's extremely rude to refer to someone as a nolla outside this student context, as it can also mean 'a nobody/a person of no importance'.
As well as nollning, there are two other terms you can use to refer to the events welcoming new students at the start of term: inspark and mottagning. These are often used by institutions which want to avoid the negative connotation which nollning has begun to get.
Nollning borde vara roligt
University initiations should be fun
Några gymnasier har förbjudit nollning
Some high schools have banned hazing