The 'tonal centre' is the note that most makes the listener feel the music has arrived back home. Each and every key has this key note - the first note played in the scale of that key. Be it major, minor or modal. A lot of tunes work on the premise that they describe a journey - starting from 'home' and returning after some detours. It's that feel of returning you need to listen for, if only doing this by ear.
It's often, but not always, the last note of a piece, and usually part of the final chord. Whether it comes at the end of a perfect or plagal cadence, it's the one that signifies finality.
Take some of the songs you know, and play/sing the last line. It's almost inevitable that the last note will be that 'home note'. The listener somehow needs to know that the piece is at its end, and not just having a bit of a rest.
By singing or listening (or playing) the notes in the question, one in particular will feel like 'the end'. There may be one or two others which allude to that, and they will be the other couple of notes contained within that home chord.
For example, in key C, obviously the C note is definitive, but E or G can feel like they are the answer. Except that G (the fifth) will feel like there's one more move to make. Same could go for C minor. C is the obvious one, but Eb or G could be the red herring.