Unilateral training involves focusing on one side of the body at a time. The benefits of this training method are that you build and require greater core strength to balance when one side of the body is bearing greater load than the other. You can really assess whether one side of the body is stronger than the other. When you do deadlifts with a barbell, if your left leg is much stronger than your right, you'll still execute the move because the stronger leg will compensate. If you're doing single leg deadlifts, however, you will know straight away if your right leg has been asleep on the job!

Why does it matter? If you keep compensating and ignoring that one side of the body is weaker,
you'll end up with over-use injuries, poor posture, soreness and fatigue.
If you do notice that one side of the body is weaker, you can plan your training to allow for extra work on that side. An extra set or extra weight to build. If you're not confident in doing this, or the difference in strength between left and right seems unusually great, see a physiotherapist! They can assess your movement and posture to diagnose what might be causing the issues and give you a program tailored to your needs.
Try:

Single Arm Chest Press
Single Leg Deadlift
Renegade Row