Just from the little bit of studying I’ve done, Centering seems to be a method of attempting to obtain what is called “acquired contemplation” which is a state of mental prayer.
It’s just a method of prayer; one among many. It is controversial, though, because (IMO) people easily misinterpret what Fr. Keating, and other Centering prayer teachers, have written about it. Their language can be a bit off-putting to some.
I haven’t actually practiced Centering prayer, nor do I plan to. Good old fashioned meditation and practicing the presence of God is what I do as far as mental prayer.