A "routine" is a way of acting and living that you do the same way, over and over again.
For example, your daily routine might include getting up at 8:00, ironing your clothes while watching TV, getting coffee at the local coffee shop on your way to work, etc.
To "settle into" a routine means to start to create a routine for yourself and to get used to it. For example:
Teaching is stressful at first, but after a few years you settle into the routine and it gets to be easier.
To "settle back into a routine" means to get used to it again after you stop doing it for a while.