Strength refers to the ability of your muscles to perform work at one time, such as lifting a heavy barbell. You build strength by putting enough resistance against your muscles that you cause damage to them. When your muscles repair themselves in response to this damage, they grow bigger. Since your heart and lungs are muscles, some people refer to your cardio capacity as cardio strength.
Many of the activities you do to build strength will also help your balance. Balance is partly a matter of developing your small stabilizer muscles that provide support and keep you steady. Free weight exercises, such as lunges and deadlifts, will help strengthen the stabilizer muscles. Even better, include some single-leg exercises, such as single-leg deadlifts and pistol squats, in your strength-training routine.