Barbell Curls are an isolation exercise that concentrates solely on the bicep muscle. Most bodybuilders use this exercise to really define the shape and size of their muscles. You cannot have good strength in the biceps by only concentrating on this one muscle in the arm.
To add more muscle and strength to your bicep region you should be focusing on doing compound exercises with a barbell such as the Bench Press or Upright Barbell Rows. These exercises work muscles across the entirety of the arm and upper back.
Since these compound exercises target multiple muscle groups in the arms, chest, shoulders and upper back. The strength and muscle distribution will spread across the arm making each muscle much stronger.
When you lift weights in compound exercises all the muscles are working together and sharing strength with each other throughout the movement of lifting and lowering the weight. This helps you keep the correct form at all times throughout the exercise.
So the strength from your upper back is helping your shoulder muscles, whose strength in-turn is helping your biceps and triceps muscles, whose strength in turn is helping the muscles in your forearms and hands. Muscles complimenting each other like this is the key to bigger strength and will also lead to faster muscle gains.
Only concentrating on one muscle will make that area of the body stronger to the detriment of the other muscles. So the other muscles around the part being exercised will big much weaker therefore it will make the strength in the part you are trying to exercise not as strong as it could be.
Read more here about the science behind gaining muscle quickly
