In simple terms, the mind-to-muscle connection is being able to consciously contract and use certain muscles during certain movements or just being able to force more contraction during isolated movements rather than just doing a movement pattern.
Bodybuilders and weightlifters learned through experience that feeling a muscle work during an exercise greatly contributed to the activity and development of that muscle. It took a while for science to back this up, but now it is more or less accepted in evidence-based research that a greater kind of muscle connection contributes to greater muscle development and involvement.
Ways to create a mind to muscle connection to a certain muscle are:
1. visualize the muscle you are working on/out.
Think about the muscle you want to work on and consciously contract that muscle.
2. Do a couple of warm-up sets to activate the muscle.
Do an isolated exercise before the main exercise to activate that muscle during the main exercise. For example: to include the glutes in the squat, do a couple of sets of single leg glute bridges.
3. Listen to or learn cues to use for your exercise.
For example, pushing your heels into a squat to use more of your posterior muscles or holding air in and creating more pressure to brace the core during a lift.
4. Increase TUT (time under tension).
Increase the time during the concentric/eccentric part of the lift or at the peak of the contraction. This will increase muscle fiber recruitment and the mind-to-muscle connection.