Frequency bandwidth is measured at the point where the op-amp gain falls to 0.707 or 1/√2 of its maximum value. This point is usually referred to as the -3dB point of the amplifier and that indicates the gain at the point where it has dropped by 3dB from its maximum value. The -3dB points at some different cases are shown here.
The open-loop configuration is going to have a higher DC gain. However, as we can see from the figure above, this configuration is extremely bandwidth limited. That means the gain starts rolling off at only a few hertz, or that the -3dB frequency is only a few hertz.
In closed-loop configuration the DC gain of the amplifier or the gain of the amplifier at zero frequency is reduced. However, the op-amp bandwidth is much wider. This basically means the frequency at which the op-amp starts rolling off has increased (remember that this is the -3dB point.)
The frequency at which the op-amp gain is only 1 or at 0dB.
A closed-loop system is a more desirable configuration when using an amplifier, unless the amplifier is used as a comparator.
(A comparator is a device which compares two voltages and switches its output to indicate which is larger.)