If something is put on a particular footing, it is defined, established, or changed in a particular way, often so that it is able to develop or exist successfully.

If you are on a particular kind of footing with someone, you have that kind of relationship with them.

You refer to your footing when you are referring to your position and how securely your feet are placed on the ground. For example, if you lose your footing, your feet slip and you fall.