There are a few layers within this concept.
Traditionally, this concept of centering relates to the core and the muscles of the core, in Pilates this is referred to as the powerhouse, physically bringing the exercise focus to the center of the body. Centering can also refer a feeling of balance within or the eternal spring of energy from which all movement emanates.
Energetically, Pilates exercises are sourced from the center.
Centering as a kinesthetic concept takes into consideration the fact that each person is built differently and has an individual center of gravity.
Taking away all other variables (lifestyle, injuries, goals, etc.) your build alone will distinctly affect how the exercise feels and how difficult or easy it is to execute. Sometimes receiving the label ‘lacking strength’ when unable to execute a movement is incorrect. The lack of success may have more to do with your distribution of body weight and build not so much your ability.
So, when unable to execute a movement right away, hold your judgements off.
Instead, stay curious and source which part of and how you could apply the principle of centering it a progress or helpful way. And as always ask for guidance from your instructor, remember Pilates is a practice.