Your core is basically the bit between tits and belt. Front and back.
Any full-body exercise will work your core and help strengthen it, so the squats you want to do will do that. To really work that mothertrunker, there are also lots of dedicated core exercises from planking to crunches to kettle bell twists and whatnot.
The video Prof has shared will work your core a great deal. Having a strong core helps with a lot of other exercise as it means you can keep form with heavier loads and longer sessions.
Iâm far from an expert, but I work my core like a bitch so happy to share any advice.