The magnitude of long jump is equal to the horizontal range obtained by the athlete during the jump which is given by \[R=\frac{u^2\sin2\theta}{g}\]
This relation shows that to obtain higher range, the launching velocity $u$ should be high. If the person jumps simply, then only vertical velocity $u_H$ will be obtained. But if he/she runs some distance, there will be some horizontal velocity $u_V$ as well. This will give the resultant velocity as \[u=\sqrt{u_H^2+u_V^2}\]
This shows that $u>u_H$. So, the athlete can get high launching speed and make the range high.
[Read: Projectile Motion]
