Everybody in the fitness industry throws this catchphrase out all the time without really explaining what it actually is. It sounds simple, but actually training it can be difficult for beginners. Mind Muscle connection can be defined as this:
Doing the movement using as much of the targeted muscle as possible and less of the muscles that are not that. Get the muscle you are trying to work/grow to do as much of the work as possible. If you do this, you will have no choice but to feel that muscle.
Now, for beginners and most intermediate lifters, there is probably a muscle group that you have a hard time feeling. For me it was chest. My shoulders would take over on every press that I did and I couldn't feel chest at all.
How to train it: find exercises that take the muscle that interferes out of the equation and do sets with higher reps, lower weight (for me it was strict cable flys). The idea behind this is literally just muscle memory. The more you use just that muscle and learn how to get it to fire, then the better you can translate it to other lifts.
The lighter weight will help you use just that muscle, and the higher reps will push more blood into those muscles which will help you feel it more than before. Always get a big stretch and big squeeze.
The long term goal here is to be able to fire that muscle effectively so that we can eventually add resistance, then we'll be able to get more stimulus from the bigger lifts.
Give this a shot if you're struggling and comment if this helps you!