https://origympersonaltrainercourses.co.uk/blog/engage-your-...

The core refers to all of the muscles which wrap around the torso and support both the pelvis and the spine, such as:

Glute muscles
Adductor muscles
Lower back muscles
Abdominal muscles and hip flexors (including the pelvic floor)
Spinal erectors
Diaphragm

Within this group of muscles, the abdominal muscles (including the rectus abdominis) are particularly important in understanding how to engage your core. The abdomen is made up of 4 sections of muscle: the transverse abdominis (TVA), the internal and external obliques and the rectus abdominis.

The TVA is the deepest section. It wraps around the waist, and acts as a stabiliser for the lower back and the core muscles, connecting the ribcage to the pelvis. On top of the TVA are the internal and external obliques. The internal and external obliques are shaped in a criss-cross across the torso and help with twisting movements. The rectus abdominis, otherwise known as the six-pack, is the anterior section of abdominal muscles which helps the upper body to bend forward...
So, what does it mean to engage your core?
Your core is engaged when all 4 sections of abdominal muscle are braced together and working with the muscles that are connected to your spine to stabilise the torso. When you know how to engage your core correctly, you will be able to stiffen your torso to support your spine whilst it bends and twists.

How to engage your core
The simplest way to engage your core is to brace yourself as if you’re expecting a strong punch to the torso, and then breathe into your stomach. Your core engages naturally right before you laugh or cough, so if you initiate one of these actions, you’ll get an idea of how it should feel when your core is engaged.

Sucking in your stomach and holding your breath are the most common mistakes people make when told to engage their core. Truthfully, this is pretty much the exact opposite of how to engage your core correctly.

Rather than sucking your stomach in, you need to focus on pulling your navel up and in towards your spine. When you do this, your abs should feel tightened but you should still be able to move and breath as normal.

A good position for engaging your core is on all fours. In this position, pull your abs up and in towards your spine and keep your torso still whilst you exhale.

Focusing on your breathing is a really important part of how to engage your core correctly. You can’t engage your core whilst holding your breath, so it’s important to keep breathing normally whilst holding your abs. The TVA engages naturally as you exhale, so you can use your breath to engage your core every time you exhale. If you pull your navel up and in during the exhale, the movement should naturally pull your stomach in and lift your torso.

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Note added at 5 hrs (2021-03-14 12:32:51 GMT)
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oops, sorry meant to delete the last bit in headline as
the rest is quoted below