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Bracing your core just means tightening the muscles around your middle so your spine stays put while you move. It is not sucking your stomach in. It's what your body does on its own right before someone pokes you in the belly or right before you cough: everything firms up at once.
To practice it: stand or lie down, take a normal breath in and then tense your abs like you are about to take a light punch to the stomach. Front, sides and lower back all tighten together. You should still be able to breathe and talk. If you can't you are squeezing too hard. Hold it for a few seconds, relax, repeat.
Once you can feel what that is - do it during exercises. Planks, squats, push-ups, anything where you don't want your lower back to sag or arch. Brace then move. It takes a bit of practice before it becomes automatic but your body will get there. Until then just check in every now and then: "is my middle tight?" If not, tighten it.
I hope this helps
