Administering the Post-War peace settlements
An example of this is the Saar Valley, which was to be administered by the LON for 15 years, and then a vote will be held. In 1935, the Saar region voted, through the plebiscite, to return to Germany rather than France.
Another job of the league was Organising mandates, which was done as part of the Mandates Commission.
This was outlined in Article 22 of the Covenant and was in relation to the colonies which were taken away from the defeated colonial powers in WW1.
The Mandatory, which was mostly Britain or France, had to submit an annual report to the League of Nations, reporting on the status and wellbeing of their mandates.