Because open-loop gain of op-amps is a function of frequency, bode plot and bandwidth are often used to describe op-amp's AC response.
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 indicateing that the gain at that point has dropped by 3dB from its maximum value.
The -3dB points at some different cases are shown below.
The open-loop configuration is going to have a higher DC gain. However, as we can see from the figure, this configuration is extremely bandwidth limited. That means the gain starts decreasing (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. It means that the frequency at which the op-amp starts rolling off has increased. The frequency at which the op-amp gain is only 1 or at 0dB, is called unity gain frequency (bandwidth).