Our iPad is asking for a 4 digit passcode that it never asked for before
Check that your iPad is not in lost mode by going here. If so, disable it by going to Find my iPhone on another iPad or iPhone or going to icloud.com on a computer and then go to Find my iPhone. Click on the device on Find my iPhone and click Lost Mode and then turn it off.

A more likely story is that someone could have enabled "Restrictions" on your iPad. There are some ways to find out this code, or to disable Restrictions all together. 

Before you do any of this, just make sure that you have Restrictions enabled by going to Settings → General → Restrictions and then click on that and if you are prompted to enter a 4 digit code, just try once more at guessing the 4 digit code. 

If it still does not work, plug in your iPad to a computer. Make a backup on iTunes with the current settings. Then follow this tutorial. This is for both Mac and PC.

Cheers and good luck!