'The merchant Jardarr has recently arrived in Ribe to find his new homestead infested by rats. You've accepted the task of helping him get rid of the rats so he can move into the house.'
Kill the Rats is a sidequest that can be started by talking to a man in the market of Ribe named Jardarr, who is having a bit of a vermin problem in his home. However, upon investigating, not all is as it seems as the vermin he is referring to are some children called The Rats.
When you reach the estate, speak to Jumper who takes charge in the conversation. You can either fight them to the death or knock them down with non-lethal hits, or give them Erlingr's farm if it's vacant after exiling/killing the family there. Once they're dealt with, return to Jardarr for your reward.
Giving The Rats the farm loses morale for your greedy and aggressive followers, but gains morale for the peaceful ones. You also lose 5 prosperity but gain 5 reputation with Ribe. Telling Ragnhildr about this also gains you 5 more reputation with Ribe.
Fighting The Rats gains morale for your aggressive followers (if you start the fight by killing Jumper via dialogue finesse check, you will also gain morale for cunning followers while honourable followers will lose morale), but loses morale for your peaceful ones.