One is Life insurance related to covering the mortgage in the event of a death. The other is Home Insurance relating to buildings & contents insurance.
Life Insurance can take a while to put in place if there is a medical condition or any medical history that needs a doctor's cert or whatever. So that can take a few weeks sometimes.
Home insurance can be done in a day/couple of days, but you need time to shop around to get insurance quotes. Sometimes you can arrange the insurance, and the insurance company will 'start' it for you closer to the time of closing. Make sure you know who needs to have a copy of the insurance and when they need it by as the closing process can be delayed by one oversight here.
If the annual policy is €400, as an example, that's just over a euro a day so having it a week early will only cost you less than a tenner.